New posts in hypergeometric-function

Proving monotonicity of this ratio of Hypergeometric functions

real-analysis gamma-function interpolation hypergeometric-function monotone-functions

Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

real-analysis sequences-and-series special-functions hypergeometric-function

Ramanujan's infinite series for $\frac{x^3(3x-2)}{(2x-1)^3}$ for all positive integers $x$

sequences-and-series hypergeometric-function

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

integration definite-integrals hypergeometric-function legendre-polynomials polylogarithm

Is this Hypergeometric Identity new?

hypergeometric-function

A series for $\log (a) \log (b)$ in terms of hypergeometric function

integration sequences-and-series logarithms hypergeometric-function

Simplifying $\int_0^1 x^{a-1} (1-x)^{b-1} \, _2F_1\left(1,d;c+d+1;2-\frac{1}{x}\right) \, dx$

statistics definite-integrals hypergeometric-function beta-function

Closed form of factorial and cascading power sum

calculus sequences-and-series combinatorics generating-functions hypergeometric-function

On the closed form for $\sum_{m=0}^\infty \prod_{n=1}^m\frac{n}{4n-1}$

sequences-and-series hypergeometric-function

A twisted hypergeometric series $\sum_{n=1}^\infty\frac{H_n}{n}\left(\frac{(2n)!}{4^n(n!)^2}\right)^2$

calculus integration definite-integrals hypergeometric-function polylogarithm

Deriving an explicit form for the nested sine integral $\int_{-\infty}^t \sin\left(A\sin(\omega t)-A\sin(\omega s)\right)e^{s-t}ds$ [closed]

real-analysis calculus integration definite-integrals hypergeometric-function

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

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

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

integration definite-integrals closed-form hypergeometric-function

On $_2F_1(\tfrac13,\tfrac23;\tfrac56;\tfrac{27}{32}) = \tfrac85$ and $_2F_1(\tfrac14,\tfrac34;\tfrac78;\tfrac{48}{49}) = \tfrac{\sqrt7}3(1+\sqrt2)$

calculus radicals hypergeometric-function experimental-mathematics

About the integral $\int_{0}^{1}\text{arctanh}(x)\arcsin(x)\frac{dx}{x}$

definite-integrals fourier-series special-functions hypergeometric-function

An identity on $\small{}_pF_q\left(\left.\begin{array}{c} a_1+1,a_2+1,\dots ,a_p+1\\ b_1+1,b_2+1,\dots ,b_q+1\end{array}\right| z\right)$

derivatives hypergeometric-function

Relation between hypergeometric and gamma functions

complex-analysis hypergeometric-function

Derivative of a generalized hypergeometric function

calculus derivatives special-functions closed-form hypergeometric-function

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

definite-integrals special-functions conjectures hypergeometric-function elliptic-integrals

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

sequences-and-series closed-form gamma-function hypergeometric-function elliptic-integrals