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Ideas for this integral: $\int \frac{\sqrt{\tan{x}}}{\sin{x}} dx$

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#calculus #integration #indefinite-integrals #elliptic-integrals
309
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Multivariate Elliptic Integral

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#integration #closed-form #multiple-integral #elliptic-integrals
538
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Evaluating the integral for a random walk

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#probability-theory #probability-distributions #random-walk #integer-lattices #elliptic-integrals
147
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Closed form of hypergeometric $\, _4F_3\left(\frac{1}{4},\frac{1}{4},\frac{3}{4},\frac{3}{4};\frac{1}{2},1,1;z\right)$

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#sequences-and-series #special-functions #closed-form #hypergeometric-function #elliptic-integrals
984
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Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

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#sequences-and-series #closed-form #gamma-function #hypergeometric-function #elliptic-integrals
179
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Calculate some integrals involving Jacobi Elliptic Functions

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#real-analysis #definite-integrals #elliptic-integrals #elliptic-functions
279
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Elliptic integrals: do they actually exist?

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#calculus #conic-sections #elliptic-curves #elliptic-integrals
83
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Separate Complete Elliptic Integral of Third Kind into Real and Imaginary Parts

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#special-functions #elliptic-integrals
89
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How to reduce this integral to complete elliptic integral of first, second, and third kind (analytically)?

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#integration #definite-integrals #greens-theorem #elliptic-integrals
496
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Elliptic integrals and $\zeta(5)$.

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#real-analysis #definite-integrals #modular-forms #elliptic-integrals
343
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Simplifying the Willmore energy of an ellipsoid

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#differential-geometry #definite-integrals #elliptic-integrals #ellipsoids
67
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Are there any ellipses with known exact circumferences and major and minor axes $a$ and $b$ and $a \neq b$?

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#geometry #conic-sections #elliptic-integrals
100
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I wonder why elliptic curve on complex field is a torus

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#geometry #elliptic-curves #elliptic-integrals
80
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Evaluating indefinite integrals from tables of definite integrals

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#integration #indefinite-integrals #elliptic-integrals
506
Views

How to find arc length of Fermat's spiral

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#calculus #arc-length #elliptic-integrals

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