New posts in special-functions

Derivative of the Meijer G-function with respect to one of its parameters

calculus complex-analysis derivatives special-functions closed-form

A Gamma limit $\lim_{n\rightarrow+\infty}\sum_{k=1}^n \left( \Gamma\bigl(\frac{k}{n}\bigr)\right)^{-k}=\frac{e^\gamma}{e^\gamma-1}$

limits summation special-functions gamma-function

Interesting Integral $\int_{-\infty}^{\infty}\frac{e^{i nx}}{\Gamma(\alpha+x) \Gamma(\beta -x)}dx$

integration special-functions improper-integrals gamma-function

Fourier transform of Bessel functions

fourier-analysis special-functions integral-transforms

Local maxima of Legendre polynomials

real-analysis special-functions orthogonal-polynomials

Quotient of gamma functions?

special-functions gamma-function

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

Integral of the modified Bessel function involving power and exponential functions

calculus integration special-functions

Feeding real or even complex numbers to the integer partition function $p(n)$?

number-theory special-functions integer-partitions

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

calculus special-functions gamma-function closed-form conjectures

Is there a name for the normal CDF function $\Phi(\cdot)$?

terminology special-functions normal-distribution

Bernoulli numbers: comparison to factorials

asymptotics special-functions analytic-number-theory bernoulli-numbers

Continuous generalization of $\sum_{k=0}^n {n \choose k} = 2^n$?

special-functions binomial-coefficients gamma-function

A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

calculus integration special-functions logarithms closed-form

Closed form for $\int_{-\infty}^0\operatorname{Ei}^3x\,dx$

calculus integration definite-integrals special-functions closed-form

Hunt for exact solutions of second order ordinary differential equations with varying coefficients.

ordinary-differential-equations special-functions

How to prove the transformation formula for Jacobi classic theta function

number-theory special-functions

Integrating a product of exponentials and error functions

calculus integration special-functions definite-integrals

Integral $\int_{-\infty}^\infty J^3_0(x) e^{i\omega x}\mathrm dx $

calculus real-analysis integration definite-integrals special-functions

A Challenging Euler Sum $\sum\limits_{n=1}^\infty \frac{H_n}{\tbinom{2n}{n}}$

sequences-and-series special-functions definite-integrals closed-form