New posts in special-functions

Polylogarithm ladders for the tribonacci and n-nacci constants

sequences-and-series special-functions golden-ratio polylogarithm

"Continuized" Taylor Series? $\sin(x)=\sum \frac{(-1)^nx^{2n+1}}{(2n+1)!}=\int_{-1}^\infty \frac{\cos(\pi n) x^{2n+1}}{G(2n+1)}dn$?

calculus integration analysis special-functions laplace-transform

infinite series of the form $\sum\limits_{k=1}^{\infty}\frac{1}{a^{k}+1}$

sequences-and-series special-functions

Inverse function of $\operatorname{li}(x)$ over $x>\mu$?

integration special-functions logarithms inverse

Is there a special value for $\frac{\zeta'(2)}{\zeta(2)} $?

sequences-and-series special-functions analytic-number-theory riemann-zeta constants

Proving $\text{Li}_3\left(-\frac{1}{3}\right)-2 \text{Li}_3\left(\frac{1}{3}\right)= -\frac{\log^33}{6}+\frac{\pi^2}{6}\log 3-\frac{13\zeta(3)}{6}$?

real-analysis sequences-and-series analysis special-functions polylogarithm

An interesting sum to infinity

calculus real-analysis sequences-and-series limits special-functions

Derivative of the Gamma function

special-functions gamma-function

How do you integrate a Bessel function? I don't want to memorize answers or use a computer, is this possible?

integration special-functions

Integral$=-\frac{4}{3}\log^3 2-\frac{\pi^2}{3}\log 2+\frac{5}{2}\zeta(3)$

real-analysis integration measure-theory definite-integrals special-functions

What would qualify as a valid reason to believe there is a closed form?

integration soft-question special-functions closed-form philosophy

Closed form for $\int_0^e\mathrm{Li}_2(\ln{x})\,dx$?

integration definite-integrals special-functions closed-form polylogarithm

Fourier transform of $\operatorname{erfc}^3\left|x\right|$

calculus integration fourier-analysis special-functions error-function

What is a special function?

special-functions definition

Proving that $\int_0^1 \frac{\log^2(x)\tanh^{-1}(x)}{1+x^2}dx=\beta(4)-\frac{\pi^2}{12}G$

integration definite-integrals special-functions polylogarithm

Prove ${\large\int}_0^1\frac{\ln(1+8x)}{x^{2/3}\,(1-x)^{2/3}\,(1+8x)^{1/3}}dx=\frac{\ln3}{\pi\sqrt3}\Gamma^3\!\left(\tfrac13\right)$

calculus derivatives definite-integrals special-functions hypergeometric-function

A closed form for a triple integral with sines and cosines

calculus integration definite-integrals special-functions

Can you recommend some books on elliptic function?

reference-request special-functions elliptic-curves elliptic-functions

Residue of $z^2 e^{1/\sin z}$ at $z=\pi$

complex-analysis special-functions physics

A triple integral dancing in the unit cube

calculus integration multivariable-calculus definite-integrals special-functions