New posts in hypergeometric-function

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

sequences-and-series hypergeometric-function polylogarithm experimental-mathematics polygamma

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

About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

reference-request summation special-functions hypergeometric-function

Integral $\int_0^1\frac{\log(x)\log(1+x)}{\sqrt{1-x}}\,dx$

calculus integration definite-integrals logarithms hypergeometric-function

Closed form for $\int_{-1}^1\frac{\ln\left(2+x\,\sqrt3\right)}{\sqrt{1-x^2}\,\left(2+x\,\sqrt3\right)^n}dx$

calculus definite-integrals closed-form conjectures hypergeometric-function

Evaluating $\int_0^1\frac{x^{2/3}(1-x)^{-1/3}}{1-x+x^2}dx$

calculus integration definite-integrals hypergeometric-function

When is ${\large\int}\frac{dx}{\left(1+x^a\right)^a}$ an elementary function?

calculus integration indefinite-integrals hypergeometric-function elementary-functions

Asymptotic behaviour of generalized hypergeometric function

asymptotics hypergeometric-function

An integral $\int_0^\infty P_s(x-1)\,e^{-x}\,dx$ involving Legendre functions

calculus integration special-functions conjectures hypergeometric-function

How to prove $4\times{_2F_1}(-1/4,3/4;7/4;(2-\sqrt3)/4)-{_2F_1}(3/4,3/4;7/4;(2-\sqrt3)/4)\stackrel?=\frac{3\sqrt[4]{2+\sqrt3}}{\sqrt2}$

calculus special-functions closed-form conjectures hypergeometric-function

Closed form for $_2F_1\left(\frac12,\frac23;\,\frac32;\,\frac{8\,\sqrt{11}\,i-5}{27}\right)$

complex-analysis special-functions closed-form hypergeometric-function

Definite integral of arcsine over square-root of quadratic

definite-integrals special-functions closed-form hypergeometric-function polylogarithm

Strange closed forms for hypergeometric functions

calculus special-functions gamma-function closed-form hypergeometric-function

An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$

definite-integrals special-functions alternative-proof hypergeometric-function legendre-polynomials

Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

definite-integrals closed-form hypergeometric-function polylogarithm polygamma

Prove ${\large\int}_0^\infty\left({_2F_1}\left(\frac16,\frac12;\frac13;-x\right)\right)^{12}dx\stackrel{\color{#808080}?}=\frac{80663}{153090}$

calculus integration special-functions improper-integrals hypergeometric-function

Is there a simpler closed form for $\sum_{n=1}^\infty\frac{(2n-1)!!\ (2n+1)!!}{4^n\ (n+2)\ (n+2)!^2}$

calculus sequences-and-series closed-form hypergeometric-function

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

A way to find a closed form of multinomial convoluted polynome.

polynomials convolution hypergeometric-function multinomial-coefficients

Hypergeometric Function divergence

convergence-divergence hypergeometric-function