mirror of
https://gerrit.wikimedia.org/r/mediawiki/extensions/Math
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94b035b26a
* Include generated tests for a better test coverage of the Math extension. * Compiles texvc in testsuite (if required) * Test generator now included * Replaces the old parser tests * Fixes whitspace issues Bug: 61090 Change-Id: Iff7eeb5ee72137492c3f6659e4d4d106e5715586
73 lines
91 KiB
Plaintext
73 lines
91 KiB
Plaintext
a:447:{i:0;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:109:"<img class="tex" alt="e^{i \pi} + 1 = 0\,\!" src="/images/math/9/e/9/9e9a547076c6820b95e439dd1a5d6a32.png" />";}i:1;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:109:"<img class="tex" alt="e^{i \pi} + 1 = 0\,\!" src="/images/math/9/e/9/9e9a547076c6820b95e439dd1a5d6a32.png" />";}i:2;a:2:{i:0;s:67:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";i:1;s:155:"<img class="tex" alt="\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!" src="/images/math/6/7/a/67aca9e0de80ac6ab651ed1097b49fe2.png" />";}i:3;a:2:{i:0;s:10:"\text{abc}";i:1;s:98:"<img class="tex" alt="\text{abc}" src="/images/math/4/6/0/46045b1f6fa9dc10a3112ba360d4d9d7.png" />";}i:4;a:2:{i:0;s:10:"\alpha\,\!";i:1;s:98:"<img class="tex" alt="\alpha\,\!" src="/images/math/4/b/c/4bc6c42bbabe567d1f2516326e52b775.png" />";}i:5;a:2:{i:0;s:15:" f(x) = x^2\,\!";i:1;s:103:"<img class="tex" alt=" f(x) = x^2\,\!" src="/images/math/3/a/5/3a5f0f03603148035120a3cba993e54f.png" />";}i:6;a:2:{i:0;s:8:"\sqrt{2}";i:1;s:96:"<img class="tex" alt="\sqrt{2}" src="/images/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" />";}i:7;a:2:{i:0;s:14:"\sqrt{1-e^2}\!";i:1;s:102:"<img class="tex" alt="\sqrt{1-e^2}\!" src="/images/math/0/4/c/04c93cf9f0a7cf697add9a2d4173a9e9.png" />";}i:8;a:2:{i:0;s:14:"\sqrt{1-z^3}\!";i:1;s:102:"<img class="tex" alt="\sqrt{1-z^3}\!" src="/images/math/1/0/8/108d6aa70c84fddabbbd3ec97f3d3ff8.png" />";}i:9;a:2:{i:0;s:1:"x";i:1;s:89:"<img class="tex" alt="x" src="/images/math/9/d/d/9dd4e461268c8034f5c8564e155c67a6.png" />";}i:10;a:2:{i:0;s:42:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";i:1;s:130:"<img class="tex" alt="\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!" src="/images/math/c/0/9/c096beaae99e2d37b4050c4ccf30fbf8.png" />";}i:11;a:2:{i:0;s:43:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";i:1;s:131:"<img class="tex" alt="\check{a}, \breve{a}, \tilde{a}, \bar{a} \!" src="/images/math/e/f/3/ef387ac79f18651dd3105d2c584b3c95.png" />";}i:12;a:2:{i:0;s:32:"\hat{a}, \widehat{a}, \vec{a} \!";i:1;s:120:"<img class="tex" alt="\hat{a}, \widehat{a}, \vec{a} \!" src="/images/math/e/a/e/eaededf26bb201c699ef1597902383c3.png" />";}i:13;a:2:{i:0;s:37:"\exp_a b = a^b, \exp b = e^b, 10^m \!";i:1;s:125:"<img class="tex" alt="\exp_a b = a^b, \exp b = e^b, 10^m \!" src="/images/math/1/9/9/199ac36bc19f7951df5041aedc1e2525.png" />";}i:14;a:2:{i:0;s:37:"\ln c, \lg d = \log e, \log_{10} f \!";i:1;s:125:"<img class="tex" alt="\ln c, \lg d = \log e, \log_{10} f \!" src="/images/math/d/5/8/d58edc12e2750302cfcdfd47f7674607.png" />";}i:15;a:2:{i:0;s:48:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";i:1;s:136:"<img class="tex" alt="\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!" src="/images/math/0/d/e/0de90ca439db043c53360a81e56e2543.png" />";}i:16;a:2:{i:0;s:34:"\arcsin h, \arccos i, \arctan j \!";i:1;s:122:"<img class="tex" alt="\arcsin h, \arccos i, \arctan j \!" src="/images/math/d/4/f/d4f41532d2a06150554f27d52b3c9479.png" />";}i:17;a:2:{i:0;s:37:"\sinh k, \cosh l, \tanh m, \coth n \!";i:1;s:125:"<img class="tex" alt="\sinh k, \cosh l, \tanh m, \coth n \!" src="/images/math/2/d/4/2d460f19d2addae865a78806e3a3afd8.png" />";}i:18;a:2:{i:0;s:91:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";i:1;s:179:"<img class="tex" alt="\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!" src="/images/math/7/f/3/7f37a94f008e914726d78b52bf7e3ff4.png" />";}i:19;a:2:{i:0;s:76:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";i:1;s:164:"<img class="tex" alt="\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!" src="/images/math/4/e/7/4e797e4c1988d0f75df043f9347214c0.png" />";}i:20;a:2:{i:0;s:35:"\sgn r, \left\vert s \right\vert \!";i:1;s:123:"<img class="tex" alt="\sgn r, \left\vert s \right\vert \!" src="/images/math/c/f/2/cf2302a36d9f76e484ea9833b583bc73.png" />";}i:21;a:2:{i:0;s:23:"\min(x,y), \max(x,y) \!";i:1;s:111:"<img class="tex" alt="\min(x,y), \max(x,y) \!" src="/images/math/6/6/8/6685fb9850f120547152b9e8f89e127d.png" />";}i:22;a:2:{i:0;s:33:"\min x, \max y, \inf s, \sup t \!";i:1;s:121:"<img class="tex" alt="\min x, \max y, \inf s, \sup t \!" src="/images/math/8/c/b/8cb6afbfa7011932573dc4fe62a6326f.png" />";}i:23;a:2:{i:0;s:31:"\lim u, \liminf v, \limsup w \!";i:1;s:119:"<img class="tex" alt="\lim u, \liminf v, \limsup w \!" src="/images/math/1/5/e/15e23ef762c80f28daef47e565900b89.png" />";}i:24;a:2:{i:0;s:35:"\dim p, \deg q, \det m, \ker\phi \!";i:1;s:123:"<img class="tex" alt="\dim p, \deg q, \det m, \ker\phi \!" src="/images/math/f/f/b/ffbfa151b5260ecb5ef79f0c87514688.png" />";}i:25;a:2:{i:0;s:41:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";i:1;s:129:"<img class="tex" alt="\Pr j, \hom l, \lVert z \rVert, \arg z \!" src="/images/math/d/d/e/dde6ad7a50f2079b6e085bccfcbe49e0.png" />";}i:26;a:2:{i:0;s:49:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";i:1;s:137:"<img class="tex" alt="dt, \operatorname{d}\!t, \partial t, \nabla\psi\!" src="/images/math/b/3/2/b32346afbfaabbd8e7e3eee827952c44.png" />";}i:27;a:2:{i:0;s:155:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";i:1;s:243:"<img class="tex" alt="dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!" src="/images/math/8/8/5/8854ea48cc731b20acb7e31b7676ab14.png" />";}i:28;a:2:{i:0;s:66:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";i:1;s:169:"<img class="tex" alt="\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y" src="/images/math/9/9/4/99434cfc81c7e2121520b25248f49eab.png" />";}i:29;a:2:{i:0;s:64:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";i:1;s:152:"<img class="tex" alt="\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!" src="/images/math/5/a/4/5a419cad96da19939591abb89e952110.png" />";}i:30;a:2:{i:0;s:62:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";i:1;s:150:"<img class="tex" alt="\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!" src="/images/math/c/3/9/c390bebffad60aca74b245dcc59a25ef.png" />";}i:31;a:2:{i:0;s:24:"s_k \equiv 0 \pmod{m} \!";i:1;s:112:"<img class="tex" alt="s_k \equiv 0 \pmod{m} \!" src="/images/math/3/5/3/353ab52b3f2c5f26ee74c81d31f2a36c.png" />";}i:32;a:2:{i:0;s:14:"a\,\bmod\,b \!";i:1;s:102:"<img class="tex" alt="a\,\bmod\,b \!" src="/images/math/e/e/6/ee6494b1a13934593f79f5874592a117.png" />";}i:33;a:2:{i:0;s:36:"\gcd(m, n), \operatorname{lcm}(m, n)";i:1;s:124:"<img class="tex" alt="\gcd(m, n), \operatorname{lcm}(m, n)" src="/images/math/6/d/9/6d966ef8f78b4ae70f97c9d14f873cfa.png" />";}i:34;a:2:{i:0;s:37:"\mid, \nmid, \shortmid, \nshortmid \!";i:1;s:125:"<img class="tex" alt="\mid, \nmid, \shortmid, \nshortmid \!" src="/images/math/3/9/e/39e442097c139a70392ae8a043a9297a.png" />";}i:35;a:2:{i:0;s:57:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";i:1;s:145:"<img class="tex" alt="\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!" src="/images/math/2/a/b/2ab6022932b3bf67498985081a9a0546.png" />";}i:36;a:2:{i:0;s:27:"+, -, \pm, \mp, \dotplus \!";i:1;s:115:"<img class="tex" alt="+, -, \pm, \mp, \dotplus \!" src="/images/math/5/c/6/5c60a256506efc42047c06ea4cba9cf3.png" />";}i:37;a:2:{i:0;s:46:"\times, \div, \divideontimes, /, \backslash \!";i:1;s:134:"<img class="tex" alt="\times, \div, \divideontimes, /, \backslash \!" src="/images/math/b/3/8/b386c20a84be6bea1495f8f4d34aaf9d.png" />";}i:38;a:2:{i:0;s:39:"\cdot, * \ast, \star, \circ, \bullet \!";i:1;s:127:"<img class="tex" alt="\cdot, * 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src="/images/math/3/0/7/30784f1f1b325970cfacabacb47b192e.png" />";}i:57;a:2:{i:0;s:64:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";i:1;s:152:"<img class="tex" alt="\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!" src="/images/math/8/c/5/8c58c414b8003f68301141b50ceadc02.png" />";}i:58;a:2:{i:0;s:52:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";i:1;s:143:"<img class="tex" alt="<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!" src="/images/math/3/4/6/346b8a9e0891b24a7433041f233be228.png" />";}i:59;a:2:{i:0;s:50:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";i:1;s:141:"<img class="tex" alt=">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!" src="/images/math/8/b/8/8b8f7a0e7ad46e494dc5b032c5558068.png" />";}i:60;a:2:{i:0;s:53:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";i:1;s:141:"<img class="tex" alt="\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!" src="/images/math/2/a/0/2a0fc5dad4cb369221b29e8a49c0e769.png" 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/>";}i:139;a:2:{i:0;s:17:"\prod_{i=1}^N x_i";i:1;s:105:"<img class="tex" alt="\prod_{i=1}^N x_i" src="/images/math/f/2/b/f2be40a3bca3b9cc59559468999c5a9d.png" />";}i:140;a:2:{i:0;s:28:"\textstyle \prod_{i=1}^N x_i";i:1;s:116:"<img class="tex" alt="\textstyle \prod_{i=1}^N x_i" src="/images/math/6/5/b/65b9b87b09704b4e4301e774de4c57ae.png" />";}i:141;a:2:{i:0;s:19:"\coprod_{i=1}^N x_i";i:1;s:107:"<img class="tex" alt="\coprod_{i=1}^N x_i" src="/images/math/d/6/8/d684b776e6e99aaa14db27115904c5bf.png" />";}i:142;a:2:{i:0;s:30:"\textstyle \coprod_{i=1}^N x_i";i:1;s:118:"<img class="tex" alt="\textstyle \coprod_{i=1}^N x_i" src="/images/math/1/4/a/14a11d376f41516ee499e2830f056523.png" />";}i:143;a:2:{i:0;s:22:"\lim_{n \to \infty}x_n";i:1;s:110:"<img class="tex" alt="\lim_{n \to \infty}x_n" src="/images/math/f/6/4/f64f3526ec6d389a67c3e13dbf609dc9.png" />";}i:144;a:2:{i:0;s:33:"\textstyle \lim_{n \to \infty}x_n";i:1;s:121:"<img class="tex" alt="\textstyle \lim_{n \to \infty}x_n" src="/images/math/1/c/0/1c00b7e0e828c0f44e484919b9e0174e.png" />";}i:145;a:2:{i:0;s:41:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:129:"<img class="tex" alt="\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx" src="/images/math/4/0/7/40764d04d428b630657f305cba34c985.png" />";}i:146;a:2:{i:0;s:34:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:122:"<img class="tex" alt="\int_{1}^{3}\frac{e^3/x}{x^2}\, dx" src="/images/math/d/5/e/d5e7d8bdc59d07349b3966578895a93f.png" />";}i:147;a:2:{i:0;s:40:"\textstyle \int\limits_{-N}^{N} e^x\, dx";i:1;s:128:"<img class="tex" alt="\textstyle \int\limits_{-N}^{N} e^x\, dx" src="/images/math/9/1/9/9194fdfb9704fa475c5ae486a56041ea.png" />";}i:148;a:2:{i:0;s:33:"\textstyle \int_{-N}^{N} e^x\, dx";i:1;s:121:"<img class="tex" alt="\textstyle \int_{-N}^{N} e^x\, dx" src="/images/math/1/7/2/1726000a5a8e3c02cea114e5b545941c.png" />";}i:149;a:2:{i:0;s:24:"\iint\limits_D \, dx\,dy";i:1;s:112:"<img class="tex" alt="\iint\limits_D \, dx\,dy" src="/images/math/4/a/b/4abac8d616c5670900504ddce25a4a4b.png" />";}i:150;a:2:{i:0;s:29:"\iiint\limits_E \, dx\,dy\,dz";i:1;s:117:"<img class="tex" alt="\iiint\limits_E \, dx\,dy\,dz" src="/images/math/6/e/9/6e9a4e709d965b32de1ab3d16aca388a.png" />";}i:151;a:2:{i:0;s:34:"\iiiint\limits_F \, dx\,dy\,dz\,dt";i:1;s:122:"<img class="tex" alt="\iiiint\limits_F \, dx\,dy\,dz\,dt" src="/images/math/4/9/0/49005f50f3ba2dfade3a265ebe363ee9.png" />";}i:152;a:2:{i:0;s:38:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:126:"<img class="tex" alt="\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy" src="/images/math/c/f/c/cfcc65ff7c8970aac316f359a9aaf928.png" />";}i:153;a:2:{i:0;s:39:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:127:"<img class="tex" alt="\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy" src="/images/math/d/6/c/d6c5bf8e05426a4b56804937b9ffb559.png" />";}i:154;a:2:{i:0;s:20:"\bigcap_{i=_1}^n E_i";i:1;s:108:"<img class="tex" alt="\bigcap_{i=_1}^n E_i" src="/images/math/8/3/d/83d87c98d958c7c2db86180b49230b65.png" />";}i:155;a:2:{i:0;s:20:"\bigcup_{i=_1}^n E_i";i:1;s:108:"<img class="tex" alt="\bigcup_{i=_1}^n E_i" src="/images/math/e/6/4/e6409717ec9d63567a34f9d1173ce2ae.png" />";}i:156;a:2:{i:0;s:15:"\frac{2}{4}=0.5";i:1;s:103:"<img class="tex" alt="\frac{2}{4}=0.5" src="/images/math/4/6/d/46dc0b34e0ab4e944a437720a4431d6c.png" />";}i:157;a:2:{i:0;s:18:"\tfrac{2}{4} = 0.5";i:1;s:106:"<img class="tex" alt="\tfrac{2}{4} = 0.5" src="/images/math/2/8/4/284667fc4a92790093aa59b61b3667a0.png" />";}i:158;a:2:{i:0;s:72:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";i:1;s:160:"<img class="tex" alt="\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a" src="/images/math/5/a/3/5a37ae94a95c7dd603c20cd4fbe8d9e9.png" />";}i:159;a:2:{i:0;s:46:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";i:1;s:134:"<img class="tex" alt="\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a" src="/images/math/6/d/0/6d099c02b3faf73f9320656217415906.png" />";}i:160;a:2:{i:0;s:60:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";i:1;s:148:"<img class="tex" alt="\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}" src="/images/math/f/a/0/fa001cd2dd438152e45a44591f235148.png" />";}i:161;a:2:{i:0;s:12:"\binom{n}{k}";i:1;s:100:"<img class="tex" alt="\binom{n}{k}" src="/images/math/6/b/2/6b2be63a1b8e310465d1b538e2d7d71b.png" />";}i:162;a:2:{i:0;s:13:"\tbinom{n}{k}";i:1;s:101:"<img class="tex" alt="\tbinom{n}{k}" src="/images/math/8/4/8/8482b29cc0af31fa35ff6bf04200b265.png" />";}i:163;a:2:{i:0;s:13:"\dbinom{n}{k}";i:1;s:101:"<img class="tex" alt="\dbinom{n}{k}" src="/images/math/c/4/4/c44601a9dbb85dfb88868c14dc54c8ef.png" />";}i:164;a:2:{i:0;s:42:"\begin{matrix} x & y \\ z & v
|
|
\end{matrix}";i:1;s:142:"<img class="tex" alt="\begin{matrix} x & y \\ z & v \end{matrix}" src="/images/math/b/9/9/b99890966e1b997497211428f8e3419d.png" />";}i:165;a:2:{i:0;s:44:"\begin{vmatrix} x & y \\ z & v
|
|
\end{vmatrix}";i:1;s:144:"<img class="tex" alt="\begin{vmatrix} x & y \\ z & v \end{vmatrix}" src="/images/math/9/2/b/92b8f0e57848a80b4babd2ba93775370.png" />";}i:166;a:2:{i:0;s:44:"\begin{Vmatrix} x & y \\ z & v
|
|
\end{Vmatrix}";i:1;s:144:"<img class="tex" alt="\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}" src="/images/math/b/b/a/bba5bfd11057dbb202307584eed8f2dc.png" />";}i:167;a:2:{i:0;s:90:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots
|
|
& \ddots & \vdots \\ 0 & \cdots &
|
|
0\end{bmatrix} ";i:1;s:210:"<img class="tex" alt="\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} " src="/images/math/8/1/a/81a12a09ac84853e3d25323b8643c630.png" />";}i:168;a:2:{i:0;s:44:"\begin{Bmatrix} x & y \\ z & v
|
|
\end{Bmatrix}";i:1;s:144:"<img class="tex" alt="\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}" src="/images/math/b/f/7/bf7244e2842c8a7d55892e229560d5c1.png" />";}i:169;a:2:{i:0;s:44:"\begin{pmatrix} x & y \\ z & v
|
|
\end{pmatrix}";i:1;s:144:"<img class="tex" alt="\begin{pmatrix} x & y \\ z & v \end{pmatrix}" src="/images/math/4/4/4/444df88e616def4e275b4e920c7b872e.png" />";}i:170;a:2:{i:0;s:63:"
|
|
\bigl( \begin{smallmatrix}
|
|
a&b\\ c&d
|
|
\end{smallmatrix} \bigr)
|
|
";i:1;s:175:"<img class="tex" alt=" \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) " src="/images/math/c/d/4/cd49bbc188dce0f93fef57312af5a106.png" />";}i:171;a:2:{i:0;s:104:"f(n) =
|
|
\begin{cases}
|
|
n/2, & \text{if }n\text{ is even} \\
|
|
3n+1, & \text{if }n\text{ is odd}
|
|
\end{cases} ";i:1;s:216:"<img class="tex" alt="f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} " src="/images/math/9/8/5/98503cc6876b22f5900297971fdd42ed.png" />";}i:172;a:2:{i:0;s:66:"
|
|
\begin{align}
|
|
f(x) & = (a+b)^2 \\
|
|
& = a^2+2ab+b^2 \\
|
|
\end{align}
|
|
";i:1;s:182:"<img class="tex" alt=" \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} " src="/images/math/2/c/5/2c50960e8bcfd9e86527a123a0c43aa2.png" />";}i:173;a:2:{i:0;s:73:"
|
|
\begin{alignat}{2}
|
|
f(x) & = (a-b)^2 \\
|
|
& = a^2-2ab+b^2 \\
|
|
\end{alignat}
|
|
";i:1;s:189:"<img class="tex" alt=" \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} " src="/images/math/f/e/4/fe45a0df3e20bc5caf718e5333678d08.png" />";}i:174;a:2:{i:0;s:68:"\begin{array}{lcl}
|
|
z & = & a \\
|
|
f(x,y,z) & = & x + y + z
|
|
\end{array}";i:1;s:184:"<img class="tex" alt="\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}" src="/images/math/9/b/f/9bf19115bb27237fa997ca93b94ad217.png" />";}i:175;a:2:{i:0;s:68:"\begin{array}{lcr}
|
|
z & = & a \\
|
|
f(x,y,z) & = & x + y + z
|
|
\end{array}";i:1;s:184:"<img class="tex" alt="\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}" src="/images/math/0/2/a/02ae32735e1e21ba3b05984289fd2763.png" />";}i:176;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"<img class="tex" alt="f(x) \,\!" src="/images/math/8/d/f/8dfae20000a042d8e9047aad1d7e171e.png" />";}i:177;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"<img class="tex" alt="= \sum_{n=0}^\infty a_n x^n " src="/images/math/6/6/3/6633d51d63b35281d030755a6b0aebb1.png" />";}i:178;a:2:{i:0;s:24:"= a_0+a_1x+a_2x^2+\cdots";i:1;s:112:"<img class="tex" alt="= a_0+a_1x+a_2x^2+\cdots" src="/images/math/f/e/3/fe3e268382fd486e8572daf895bd4c9d.png" />";}i:179;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"<img class="tex" alt="f(x) \,\!" src="/images/math/8/d/f/8dfae20000a042d8e9047aad1d7e171e.png" />";}i:180;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"<img class="tex" alt="= \sum_{n=0}^\infty a_n x^n " src="/images/math/6/6/3/6633d51d63b35281d030755a6b0aebb1.png" />";}i:181;a:2:{i:0;s:25:"= a_0 +a_1x+a_2x^2+\cdots";i:1;s:113:"<img class="tex" alt="= a_0 +a_1x+a_2x^2+\cdots" src="/images/math/f/e/3/fe3e268382fd486e8572daf895bd4c9d.png" />";}i:182;a:2:{i:0;s:70:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";i:1;s:158:"<img class="tex" alt="\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}" src="/images/math/6/3/4/6349be04b3562fc215c7a4e130422a96.png" />";}i:183;a:2:{i:0;s:89:"
|
|
\begin{array}{|c|c||c|} a & b & S \\
|
|
\hline
|
|
0&0&1\\
|
|
0&1&1\\
|
|
1&0&1\\
|
|
1&1&0\\
|
|
\end{array}
|
|
";i:1;s:249:"<img class="tex" alt=" \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} " src="/images/math/9/1/5/9151e94ef2bb52c18176dbe4c11921ed.png" />";}i:184;a:2:{i:0;s:15:"( \frac{1}{2} )";i:1;s:103:"<img class="tex" alt="( \frac{1}{2} )" src="/images/math/4/0/a/40ad9d3d1fc9a61e16d22d7e3f854fec.png" />";}i:185;a:2:{i:0;s:28:"\left ( \frac{1}{2} \right )";i:1;s:116:"<img class="tex" alt="\left ( \frac{1}{2} \right )" src="/images/math/2/8/b/28bcd5b82ce0e92b25e8a0b4bd5be215.png" />";}i:186;a:2:{i:0;s:28:"\left ( \frac{a}{b} \right )";i:1;s:116:"<img class="tex" alt="\left ( \frac{a}{b} \right )" src="/images/math/2/9/0/2905969500b40b2f2c7078206e7e0e81.png" />";}i:187;a:2:{i:0;s:75:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";i:1;s:163:"<img class="tex" alt="\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack" src="/images/math/7/c/b/7cb5a74153ec87cdda6b92669ba685e1.png" />";}i:188;a:2:{i:0;s:77:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";i:1;s:165:"<img class="tex" alt="\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace" src="/images/math/8/0/5/805b2e61cb380736d5366bccb844b1c7.png" />";}i:189;a:2:{i:0;s:40:"\left \langle \frac{a}{b} \right \rangle";i:1;s:128:"<img class="tex" alt="\left \langle \frac{a}{b} \right \rangle" src="/images/math/d/0/6/d06e733ce705ed26a7e048dbd2945371.png" />";}i:190;a:2:{i:0;s:72:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";i:1;s:160:"<img class="tex" alt="\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|" src="/images/math/8/0/9/809fc4791f12abb16a5f9611a43469f9.png" />";}i:191;a:2:{i:0;s:85:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";i:1;s:173:"<img class="tex" alt="\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil" 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S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:359;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:198:"<img class="tex" alt="( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} " src="/images/math/f/6/d/f6d35e69f3593017cdd38fbf8e798a9f.png" />";}i:360;a:2:{i:0;s:57:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:145:"<img class="tex" alt="\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/0/f/3/0f3f1a7580395190da1d7e7bba5a72e6.png" />";}i:361;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:362;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"<img class="tex" alt="\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}" src="/images/math/3/9/a/39a571d0f6a01877c10d8790a5943eab.png" />";}i:363;a:2:{i:0;s:68:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:156:"<img class="tex" alt="\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/2/2/9/229ef1d17720ecf0b771d0783ce81c24.png" />";}i:364;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:365;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"<img class="tex" alt="\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}" src="/images/math/3/9/a/39a571d0f6a01877c10d8790a5943eab.png" />";}i:366;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"<img class="tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:367;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"<img class="tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:368;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"<img class="tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:369;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"<img class="tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:370;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"<img class="tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:371;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"<img class="tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:372;a:2:{i:0;s:20:"\overset{\frown}{AB}";i:1;s:108:"<img class="tex" alt="\overset{\frown}{AB}" src="/images/math/8/7/4/8748475980cbfc9c9028b4b298d2f438.png" />";}i:373;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"<img class="tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:374;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"<img class="tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:375;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"<img class="tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:376;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"<img class="tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:377;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";i:1;s:144:"<img class="tex" alt="2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:378;a:2:{i:0;s:56:"2 = \left(
|
|
\frac{\left(3-x\right) \times 2}{3-x}
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|
\right)";i:1;s:152:"<img class="tex" alt="2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:379;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"<img class="tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:380;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"<img class="tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:381;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";i:1;s:149:"<img class="tex" alt="\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy" src="/images/math/4/4/6/4465ba032469b775777205effe6cdc0f.png" />";}i:382;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
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= \int_a^x f(y)(x-y)\,dy";i:1;s:153:"<img class="tex" alt="\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy" src="/images/math/4/4/6/4465ba032469b775777205effe6cdc0f.png" />";}i:383;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"<img class="tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:384;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"<img class="tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:385;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"<img class="tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:386;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"<img class="tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:387;a:2:{i:0;s:78:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:166:"<img class="tex" alt="\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}" src="/images/math/5/c/d/5cd6041b50d619f041f121baea301898.png" />";}i:388;a:2:{i:0;s:79:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
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{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:171:"<img class="tex" alt="\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}" src="/images/math/5/c/d/5cd6041b50d619f041f121baea301898.png" />";}i:389;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"<img class="tex" alt="u'' + p(x)u' + q(x)u=f(x),\quad x>a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:390;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"<img class="tex" alt="u'' + p(x)u' + q(x)u=f(x),\quad x>a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:391;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";i:1;s:149:"<img class="tex" alt="|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)" src="/images/math/2/e/a/2eac34dbc8ebbccb22ce8dfe9d5c1a86.png" />";}i:392;a:2:{i:0;s:61:"|\bar{z}| = |z|,
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|(\bar{z})^n| = |z|^n,
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\arg(z^n) = n \arg(z)";i:1;s:157:"<img class="tex" alt="|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)" src="/images/math/2/e/a/2eac34dbc8ebbccb22ce8dfe9d5c1a86.png" />";}i:393;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"<img class="tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:394;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"<img class="tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:395;a:2:{i:0;s:170:"\phi_n(\kappa)
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= \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:262:"<img class="tex" alt="\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR" src="/images/math/7/f/b/7fb11db1e8b5890998b2f0f59f0e3d60.png" />";}i:396;a:2:{i:0;s:170:"\phi_n(\kappa) =
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\frac{1}{4\pi^2\kappa^2} \int_0^\infty
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\frac{\sin(\kappa R)}{\kappa R}
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\frac{\partial}{\partial R}
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\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:274:"<img class="tex" alt="\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR" src="/images/math/7/f/b/7fb11db1e8b5890998b2f0f59f0e3d60.png" />";}i:397;a:2:{i:0;s:86:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:174:"<img class="tex" alt="\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}" src="/images/math/8/f/7/8f72d606f5f91bd51583a0a08b36eed9.png" />";}i:398;a:2:{i:0;s:86:"\phi_n(\kappa) =
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0.033C_n^2\kappa^{-11/3},\quad
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\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:182:"<img class="tex" alt="\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}" src="/images/math/8/f/7/8f72d606f5f91bd51583a0a08b36eed9.png" />";}i:399;a:2:{i:0;s:100:"f(x) = \begin{cases}1 & -1 \le x < 0 \\
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\frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";i:1;s:207:"<img class="tex" alt="f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}" src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:400;a:2:{i:0;s:104:"
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f(x) =
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\begin{cases}
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1 & -1 \le x < 0 \\
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\frac{1}{2} & x = 0 \\
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1 - x^2 & \text{otherwise}
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\end{cases}
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";i:1;s:235:"<img class="tex" alt=" f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise} \end{cases} " src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:401;a:2:{i:0;s:122:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";i:1;s:210:"<img class="tex" alt="{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}" src="/images/math/c/0/2/c02cbc6ec9c57aca74ebc3a0314dea79.png" />";}i:402;a:2:{i:0;s:123:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
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= \sum_{n=0}^\infty
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\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
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\frac{z^n}{n!}";i:1;s:223:"<img class="tex" alt="{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} \frac{z^n}{n!}" src="/images/math/c/0/2/c02cbc6ec9c57aca74ebc3a0314dea79.png" />";}i:403;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"<img class="tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:404;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"<img class="tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:405;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"<img class="tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:406;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"<img class="tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:407;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"<img class="tex" alt="V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]" src="/images/math/6/2/4/624bfa733e479dff276edfdc7b1b8f6a.png" />";}i:408;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"<img class="tex" alt="V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]" src="/images/math/6/2/4/624bfa733e479dff276edfdc7b1b8f6a.png" />";}i:409;a:2:{i:0;s:167:"\begin{align}
|
|
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\
|
|
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
|
|
\end{align}";i:1;s:291:"<img class="tex" alt="\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:410;a:2:{i:0;s:168:"\begin{align}
|
|
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\
|
|
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
|
|
\end{align}";i:1;s:292:"<img class="tex" alt="\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:411;a:2:{i:0;s:172:" with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags. [[Image:foobar.jpg|thumb|<math>2+2";i:1;s:259:"<strong class='error texerror'>Failed to parse (syntax error): with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped &lt;math&gt; tags. [[Image:foobar.jpg|thumb|<math>2+2</strong>
|
|
";}i:412;a:2:{i:0;s:66:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2";i:1;s:160:"<img class="tex" alt=" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2" src="/images/math/4/b/1/4b1d6eacd0bcc60a0aadf0d34626ee74.png" />";}i:413;a:2:{i:0;s:41:"<script>alert(document.cookies);</script>";i:1;s:141:"<img class="tex" alt="<script>alert(document.cookies);</script>" src="/images/math/5/9/f/59f1117d63b4ce95a694d44b588f0840.png" />";}i:414;a:2:{i:0;s:11:"\widehat{x}";i:1;s:99:"<img class="tex" alt="\widehat{x}" src="/images/math/9/9/8/998309e831dfb051f233c92b4b8a825b.png" />";}i:415;a:2:{i:0;s:13:"\widetilde{x}";i:1;s:101:"<img class="tex" alt="\widetilde{x}" src="/images/math/e/9/e/e9e91996778a6d6f5cdf4cc951955206.png" />";}i:416;a:2:{i:0;s:9:"\euro 200";i:1;s:97:"<img class="tex" alt="\euro 200" src="/images/math/1/8/8/18867d4c568a19ae7b2388346e504ec3.png" />";}i:417;a:2:{i:0;s:8:"\geneuro";i:1;s:96:"<img class="tex" alt="\geneuro" src="/images/math/9/8/b/98b63c235ee187a38267e0e170b10e9d.png" />";}i:418;a:2:{i:0;s:14:"\geneuronarrow";i:1;s:102:"<img class="tex" alt="\geneuronarrow" src="/images/math/a/a/4/aa4a1ed370f4ee705c6930384bf89502.png" />";}i:419;a:2:{i:0;s:12:"\geneurowide";i:1;s:100:"<img class="tex" alt="\geneurowide" src="/images/math/4/4/0/4404468e6187fb04e4f7e1f15e550825.png" />";}i:420;a:2:{i:0;s:13:"\officialeuro";i:1;s:101:"<img class="tex" alt="\officialeuro" src="/images/math/d/7/0/d708de0eed23dbd6f02b99ea9073547b.png" />";}i:421;a:2:{i:0;s:8:"\digamma";i:1;s:96:"<img class="tex" alt="\digamma" src="/images/math/2/f/0/2f057b6e514c8ca2d9cf9a3e549f8865.png" />";}i:422;a:2:{i:0;s:21:"\Coppa\coppa\varcoppa";i:1;s:109:"<img class="tex" alt="\Coppa\coppa\varcoppa" src="/images/math/8/3/0/8308ee5003aa36112414cad8ef874f85.png" />";}i:423;a:2:{i:0;s:8:"\Digamma";i:1;s:96:"<img class="tex" alt="\Digamma" src="/images/math/5/c/f/5cfd6e5df6c87798542dca2e22c1e7cb.png" />";}i:424;a:2:{i:0;s:12:"\Koppa\koppa";i:1;s:100:"<img class="tex" alt="\Koppa\koppa" src="/images/math/5/2/5/52593a0cdac178d165985ac014788b97.png" />";}i:425;a:2:{i:0;s:12:"\Sampi\sampi";i:1;s:100:"<img class="tex" alt="\Sampi\sampi" src="/images/math/e/9/d/e9dabb19e4c27bf23d3c2a3629474562.png" />";}i:426;a:2:{i:0;s:24:"\Stigma\stigma\varstigma";i:1;s:112:"<img class="tex" alt="\Stigma\stigma\varstigma" src="/images/math/7/b/9/7b9233276816994a33a5e968202cef6e.png" />";}i:427;a:2:{i:0;s:17:"\text{next years}";i:1;s:105:"<img class="tex" alt="\text{next years}" src="/images/math/6/6/9/6691dbc0b36631a68b78dd5ace256d80.png" />";}i:428;a:2:{i:0;s:18:"\text{next year's}";i:1;s:111:"<img class="tex" alt="\text{next year's}" src="/images/math/2/3/6/236fd262b1976d04bc0e7a969d61aede.png" />";}i:429;a:2:{i:0;s:18:"\text{`next' year}";i:1;s:111:"<img class="tex" alt="\text{`next' year}" src="/images/math/0/5/8/05854b483a833f067cb6ae72319b44bc.png" />";}i:430;a:2:{i:0;s:6:"\sin x";i:1;s:94:"<img class="tex" alt="\sin x" src="/images/math/c/d/b/cdba58911c590ced3e2435dfa39f6873.png" />";}i:431;a:2:{i:0;s:7:"\sin(x)";i:1;s:95:"<img class="tex" alt="\sin(x)" src="/images/math/3/e/2/3e21673ce6c9b09f9ec50b7237248576.png" />";}i:432;a:2:{i:0;s:7:"\sin{x}";i:1;s:95:"<img class="tex" alt="\sin{x}" src="/images/math/f/b/5/fb5551723991d4dcb974a23c162ae813.png" />";}i:433;a:2:{i:0;s:9:"\sin x \,";i:1;s:97:"<img class="tex" alt="\sin x \," src="/images/math/7/6/a/76a8e1a01bd233c1e4e16d63b2bbf939.png" />";}i:434;a:2:{i:0;s:10:"\sin(x) \,";i:1;s:98:"<img class="tex" alt="\sin(x) \," src="/images/math/1/6/c/16c69b0a3658d3b398f72c518d869a03.png" />";}i:435;a:2:{i:0;s:10:"\sin{x} \,";i:1;s:98:"<img class="tex" alt="\sin{x} \," src="/images/math/8/3/9/839639707da39f691e702c2399cbf943.png" />";}i:436;a:2:{i:0;s:6:"\sen x";i:1;s:94:"<img class="tex" alt="\sen x" src="/images/math/f/b/8/fb82a78d580396c62cecb4cf018f3769.png" />";}i:437;a:2:{i:0;s:7:"\sen(x)";i:1;s:95:"<img class="tex" alt="\sen(x)" src="/images/math/8/3/a/83a10e6756c8e59055178dc1f593130a.png" />";}i:438;a:2:{i:0;s:7:"\sen{x}";i:1;s:95:"<img class="tex" alt="\sen{x}" src="/images/math/0/4/f/04fde4f7a7e478015066f378050b1979.png" />";}i:439;a:2:{i:0;s:9:"\sen x \,";i:1;s:97:"<img class="tex" alt="\sen x \," src="/images/math/0/a/c/0ac592b8f31b4698766c50c532f446a7.png" />";}i:440;a:2:{i:0;s:10:"\sen(x) \,";i:1;s:98:"<img class="tex" alt="\sen(x) \," src="/images/math/b/b/5/bb5469d24fcdd52aa60cb9ee90ba697d.png" />";}i:441;a:2:{i:0;s:10:"\sen{x} \,";i:1;s:98:"<img class="tex" alt="\sen{x} \," src="/images/math/d/4/8/d4882a4bcf5db1da3e30d905da8b394e.png" />";}i:442;a:2:{i:0;s:18:"\operatorname{sen}";i:1;s:106:"<img class="tex" alt="\operatorname{sen}" src="/images/math/f/a/9/fa9660c7eb053ca8d3c9a87fa86635d9.png" />";}i:443;a:2:{i:0;s:11:"\dot \vec B";i:1;s:99:"<img class="tex" alt="\dot \vec B" src="/images/math/e/6/4/e64939568ecb506a86a392373cec0458.png" />";}i:444;a:2:{i:0;s:18:"\tilde \mathcal{M}";i:1;s:106:"<img class="tex" alt="\tilde \mathcal{M}" src="/images/math/5/5/0/55072ce6ef8c840c4b7687bd8a028bde.png" />";}i:445;a:2:{i:0;s:0:"";i:1;s:160:"<strong class='error texerror'>Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): </strong>
|
|
";}i:446;a:2:{i:0;s:1:" ";i:1;s:161:"<strong class='error texerror'>Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): </strong>
|
|
";}} |