New posts in elliptic-integrals

Looking for a closed form for a ${}_4 F_3\left(\ldots,1\right)$

sequences-and-series special-functions closed-form hypergeometric-function elliptic-integrals

Identity concerning complete elliptic integrals

calculus alternative-proof elliptic-integrals

Is this Lauricella $\text F_\text D$ to hypergeometric R, from DLMF, conversion formula correct?

solution-verification special-functions hypergeometric-function elliptic-integrals reduction-formula

Solving what Mathematica could not

integration definite-integrals elliptic-integrals

Can the complete elliptic integrals of the third kind to be expressed in series?

sequences-and-series elliptic-integrals

The term “elliptic”

terminology elliptic-curves elliptic-integrals noneuclidean-geometry

Evaluation of complete elliptic integrals $K(k) $ for $k=\tan(\pi/8),\sin(\pi/12)$

calculus integration definite-integrals elliptic-integrals

Interesting closed form for $\int_0^{\frac{\pi}{2}}\frac{1}{\left(\frac{1}{3}+\sin^2{\theta}\right)^{\frac{1}{3}}}\;d\theta$

calculus definite-integrals closed-form gamma-function elliptic-integrals

Simplify $\frac{_3F_2\left(\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2};\frac{3}{4}\right)}{\Pi\left(\frac{1}{4}\big|\frac{1}{\sqrt{3}}\right)}$

calculus closed-form conjectures hypergeometric-function elliptic-integrals

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

integration definite-integrals closed-form hypergeometric-function elliptic-integrals

Conjectured closed form for $\int_0^1x^{2\,q-1}\,K(x)^2dx$ where $K(x)$ is the complete elliptic integral of the 1ˢᵗ kind

calculus definite-integrals closed-form conjectures elliptic-integrals

Is this function decreasing on $(0,1)$?

real-analysis reference-request special-functions elliptic-integrals

How to integrate $ \int \frac{x}{\sqrt{x^4+10x^2-96x-71}}dx$?

calculus integration algorithms elliptic-integrals

Arithmetic-geometric mean of 3 numbers

calculus sequences-and-series reference-request closed-form elliptic-integrals