New posts in special-functions

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

logarithms special-functions closed-form conjectures polylogarithm

How does Lambert's W behave near ∞?

analysis asymptotics special-functions

Is there any proof that the Riemann Zeta function is not elementary?

special-functions riemann-zeta

Computing a limit involving Gammaharmonic series

calculus sequences-and-series limits special-functions gamma-function

Is this Lauricella $\text F_\text D$ to hypergeometric R, from DLMF, conversion formula correct?

solution-verification special-functions hypergeometric-function elliptic-integrals reduction-formula

On the completeness of the generalized Laguerre polynomials

reference-request special-functions orthogonal-polynomials

About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

reference-request summation special-functions hypergeometric-function

Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?

calculus approximation gamma-function numerical-methods special-functions

How to solve the Brioschi quintic in terms of elliptic functions?

polynomials special-functions modular-forms elliptic-functions

Extract real and imaginary parts of $\operatorname{Li}_2\left(i\left(2\pm\sqrt3\right)\right)$

calculus complex-analysis special-functions closed-form polylogarithm

The roots of Hermite polynomials are all real?

calculus special-functions orthogonal-polynomials

Proving $\int_{\sqrt{5/7}}^1 \frac{(\pi-3\arctan\sqrt{\frac{2x^2-1}{3x^2-2}})\arctan x}{\sqrt{2x^2-1}(3x^2-1)} dx = \frac{\pi^3}{672}$

integration definite-integrals special-functions

Convexity of $\theta(q)$

complex-analysis analysis special-functions elliptic-functions theta-functions

Calculate integrals involving gamma function

calculus integration special-functions definite-integrals gamma-function

Generalizing two infinite products for $\operatorname{sinc}(x)$ and their 'dual' infinite product

trigonometry convergence-divergence special-functions closed-form infinite-product

Evaluating $\int_{T}^{\infty} \exp\left[\beta - \phi t \right]t^{-\frac{3}{2}} \log ^{\kappa}(t) \mbox{d}t$

calculus integration improper-integrals special-functions

Evaluation of $\sum_{x=0}^\infty e^{-x^2}$

sequences-and-series integration special-functions closed-form

Need help with $\int_0^\infty x^{-\frac{3}{2}}\ \text{Li}_{\sqrt{2}}(-x)\ dx$

special-functions improper-integrals closed-form

Prove that $\int_0^\infty\frac1{x^x}\, dx<2$

integration definite-integrals summation special-functions

Prove $\gamma_1\left(\frac34\right)-\gamma_1\left(\frac14\right)=\pi\,\left(\gamma+4\ln2+3\ln\pi-4\ln\Gamma\left(\frac14\right)\right)$

calculus special-functions