Newbetuts

Accurate identities related to $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^3}x^n$ and $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^4}x^n$

A known closed form for Borchardt mean (generalization of AGM) - why doesn't it work?

A Nasty Elliptic Integral

Numerical Integral of Complete Elliptic Integral

A tough series related with a hypergeometric function with quarter integer parameters

How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?

Proof of an Elliptic Integral Relation

How do I integrate $\frac{\sqrt{1-k^2\sin^2 x}}{\sin x}$

Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

How to find arc length of Fermat's spiral

A curve with arc length equal to the elliptic integral of the first kind. What's the area?

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

Closed-form expression for an iterated integral

The integral of an elliptic integral: $\int_{0}^{1}\frac{x\mathbf{K}^2\left ( x \right )}{\sqrt{1-x^{2}}}\mathrm{d}x$

Legendre relations for elliptic integrals with null imaginary part

New posts in elliptic-integrals

Real part of elliptic integral

Elliptic Integrals & Gamma Functions of Rational values.

Indefinite integral $\int \arcsin \left(k\sin x\right) dx$

Infinite series with harmonic numbers related to elliptic integrals

Accurate identities related to $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^3}x^n$ and $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^4}x^n$

A known closed form for Borchardt mean (generalization of AGM) - why doesn't it work?

A Nasty Elliptic Integral

Numerical Integral of Complete Elliptic Integral

A tough series related with a hypergeometric function with quarter integer parameters

How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?

Proof of an Elliptic Integral Relation

How do I integrate $\frac{\sqrt{1-k^2\sin^2 x}}{\sin x}$

Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

How to find arc length of Fermat's spiral

A curve with arc length equal to the elliptic integral of the first kind. What's the area?

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

Closed-form expression for an iterated integral

The integral of an elliptic integral: $\int_{0}^{1}\frac{x\mathbf{K}^2\left ( x \right )}{\sqrt{1-x^{2}}}\mathrm{d}x$

Legendre relations for elliptic integrals with null imaginary part