New posts in special-functions

Connection between Hermite & Legendre polynomials

special-functions orthogonal-polynomials

A very odd-looking statement about $\zeta(3)$ and $\text{Li}_2\left(\frac{1}{\varphi^2}\right)$

reference-request special-functions riemann-zeta

About the asymptotic formula of Bessel function

special-functions asymptotics

An interesting identity involving Jacobi $\theta_4$ and $\zeta(2)$

sequences-and-series fourier-series special-functions alternative-proof theta-functions

Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

integration trigonometry special-functions exponential-function closed-form

Proof that $x \Phi(x) + \Phi'(x) \geq 0$ $\forall x$, where $\Phi$ is the normal CDF

probability inequality special-functions

How to calclulate a derivate of a hypergeometric function w.r.t. one of its parameters?

calculus derivatives special-functions closed-form hypergeometric-function

Maximal logarithmic likelihood function of the Student-t distribution

real-analysis inequality special-functions maxima-minima gamma-function

How to prove $\int_0^\pi\frac{\ln(2+\cos\phi)}{\sqrt{2+\cos\phi}}d\phi=\frac{\ln3}{\sqrt3}K\left(\sqrt{\frac23}\right)$?

integration definite-integrals special-functions closed-form elliptic-integrals

Closed-form of $\int_0^1 B_n(x)\psi(x+1)\,dx$

integration polynomials definite-integrals special-functions closed-form

The graph of $x^{n}+y^{n}=r^{n}$ for sufficiently large $n$

special-functions

Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$

calculus integration definite-integrals special-functions polylogarithm

What even *are* elliptic functions?

complex-analysis special-functions analytic-number-theory elliptic-integrals elliptic-functions

Addition theorems for elliptic functions: is there a painless way?

complex-analysis special-functions elliptic-functions

Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$ [duplicate]

calculus sequences-and-series special-functions polygamma

Dilogarithm inversion formula: $ \text{Li}_2(z) + \text{Li}_2(1/z) = -\zeta(2) - \log^2(-z)/2$

real-analysis integration special-functions

Integrate $\int_0^1 \frac{\ln(1+x^a)}{1+x}\, dx$

calculus sequences-and-series analysis special-functions

A "relative" of the exponential function

power-series exponential-function special-functions volume

Hermite's solution of the general quintic in terms of theta functions

reference-request polynomials special-functions theta-functions

Prove that sum is finite

sequences-and-series convergence-divergence special-functions summation divergent-series