New posts in special-functions

Closed form for $\int_0^\infty\left(\int_0^1\frac1{\sqrt{1-y^2}\sqrt{1+x^2\,y^2}}\mathrm dy\right)^3\mathrm dx.$

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

Is there an Inverse Gamma $\Gamma^{-1} (z) $ function?

analysis special-functions

How to accurately calculate the error function $\operatorname{erf}(x)$ with a computer?

statistics algorithms numerical-methods special-functions

Series of logarithms $\sum\limits_{k=1}^\infty \ln(k)$ (Ramanujan summation?)

sequences-and-series special-functions logarithms divergent-series

elliptic functions on the 17 wallpaper groups

special-functions symmetric-groups elliptic-functions tessellations

Fourier transform of the indicator of the unit ball

analysis fourier-analysis special-functions

Generalized Owen's T function

probability indefinite-integrals special-functions gaussian-integral

Inverse of $y=xe^x$

special-functions exponentiation lambert-w

Evaluating $\sum_{n=0}^\infty\frac{(1/2)_n}{n!}(H_n-H_{n-1/2})$

sequences-and-series special-functions hypergeometric-function harmonic-numbers pochhammer-symbol

Prove $_2F_1\left(\frac13,\frac13;\frac56;-27\right)\stackrel{\color{#808080}?}=\frac47$

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

Interesting log sine integrals $\int_0^{\pi/3} \log^2 \left(2\sin \frac{x}{2} \right)dx= \frac{7\pi^3}{108}$

calculus integration special-functions definite-integrals

Weber-type integral

integration special-functions error-function

On Shanks' quartic approximation $\pi \approx \frac{6}{\sqrt{3502}}\ln(2u)$

number-theory special-functions approximation pi

Fractional Calculus: Motivation and Foundations.

soft-question special-functions foundations motivation fractional-calculus

Proof that $\sum\limits_{k=1}^\infty\frac{a_1a_2\cdots a_{k-1}}{(x+a_1)\cdots(x+a_k)}=\frac{1}{x}$ regarding $\zeta(3)$ and Apéry's proof

sequences-and-series special-functions power-series riemann-zeta

Proving a known zero of the Riemann Zeta has real part exactly 1/2

complex-analysis special-functions riemann-zeta conjectures riemann-hypothesis

Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$

integration complex-analysis definite-integrals special-functions gamma-function

Closed form for integral of integer powers of Sinc function

integration definite-integrals special-functions improper-integrals closed-form

Are elementary and generalized hypergeometric functions sufficient to express all algebraic numbers?

calculus algebraic-number-theory special-functions hypergeometric-function radicals

A closed form for $\int_0^1{_2F_1}\left(-\frac{1}{4},\frac{5}{4};\,1;\,\frac{x}{2}\right)^2dx$

calculus integration special-functions closed-form hypergeometric-function