New posts in special-functions

Continued fraction expansion related to exponential generating function

algorithms power-series special-functions continued-fractions bernoulli-numbers

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

calculus special-functions closed-form polylogarithm

Integral $\int_{-1}^{1} \frac{1}{(1+u^2)^{n/2}} \exp{\left(-2\pi \frac{a^2+b^2}{1+u^2}\right)} \exp{\left(-4\pi i ab \frac{u}{1+u^2}\right)} du $

calculus integration definite-integrals special-functions complex-integration

Integral with exp and erf

calculus special-functions definite-integrals

Orthogonality of Bessel functions

special-functions

Problem with the Dirichlet Eta Function

sequences-and-series special-functions

Fourier transform of squared exponential integral $\operatorname{Ei}^2(-|x|)$

calculus integration definite-integrals fourier-analysis special-functions

Derivatives of the Riemann zeta function at $s=0$

complex-analysis inequality special-functions riemann-zeta

Solving higher order logarithms integrals without the beta function

calculus integration definite-integrals special-functions

Indefinite integral $\int \arcsin \left(k\sin x\right) dx$

special-functions closed-form elliptic-integrals polylogarithm

Proving $\sum _{k=1}^n \frac{(-1)^{k-1} 16^k (k-1)! k! (k+n-1)!}{((2 k)!)^2 (n-k)!}=\frac{4}{n}\sum _{k=1}^n \frac{1}{2 k-1}$

integration definite-integrals summation special-functions

Infinite series with harmonic numbers related to elliptic integrals

sequences-and-series special-functions generating-functions harmonic-numbers elliptic-integrals

The value of the trilogarithm at $\frac{1}{2}$

special-functions functional-equations

How to evaluate the following integral using hypergeometric function?

calculus integration special-functions

Any even elliptic function can be written in terms of the Weierstrass $\wp$ function

complex-analysis analysis special-functions elliptic-functions

The partial fraction expansion of $\frac{1}{x^n - 1}$.

special-functions partial-fractions

Variations on the Stirling's formula for $\Gamma(z)$

complex-analysis special-functions asymptotics gamma-function

What counts as a "known" function

functions soft-question special-functions

$\frac{\mathrm d^2 \log(\Gamma (z))}{\mathrm dz^2} = \sum\limits_{n = 0}^{\infty} \frac{1}{(z+n)^2}$

complex-analysis special-functions

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

calculus integration definite-integrals special-functions residue-calculus