Newbetuts

Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

Prove the roots of these exponential functions are integers?

How to prove asymptotic limit of an incomplete Gamma function

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

Proof of an Elliptic Integral Relation

Derivative of a generalized hypergeometric function

A conjectured asymptotic expansion of a function related to the sine and cosine integrals

Evaluate $\int_0^1 \frac{\ln(1+bx)}{1+x} dx $

Bessel function integral and Mellin transform

Integral $ \int_{0}^{\infty} \ln x\left[\ln \left( \frac{x+1}{2} \right) - \frac{1}{x+1} - \psi \left( \frac{x+1}{2} \right) \right] \mathrm{d}x $

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

Inverse of the polylogarithm

Mellin transform of digamma function

Can any continuous function be represented as an infinite polynomial?

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

New posts in special-functions

$\frac{1}{e^x-1}$, $\Gamma(s)$, $\zeta(s)$, and $x^{s-1}$

The series $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}\mbox{sech}\left(\frac{(2n-1)\pi}{2}\right)$

An $\operatorname{erfi}(x)e^{-x^2}$ integral

Evaluating an integral of unit step function?

Gauss Digamma theorem proof

Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

Prove the roots of these exponential functions are integers?

How to prove asymptotic limit of an incomplete Gamma function

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

Proof of an Elliptic Integral Relation

Derivative of a generalized hypergeometric function

A conjectured asymptotic expansion of a function related to the sine and cosine integrals

Evaluate $\int_0^1 \frac{\ln(1+bx)}{1+x} dx $

Bessel function integral and Mellin transform

Integral $ \int_{0}^{\infty} \ln x\left[\ln \left( \frac{x+1}{2} \right) - \frac{1}{x+1} - \psi \left( \frac{x+1}{2} \right) \right] \mathrm{d}x $

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

Inverse of the polylogarithm

Mellin transform of digamma function

Can any continuous function be represented as an infinite polynomial?

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