New posts in special-functions

The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$

special-functions logarithms mathematica closed-form transcendental-equations

Algorithm to compute Gamma function

algorithms numerical-methods special-functions gamma-function

Find the value of $\int_{0}^{\infty}\frac{x^3}{e^x-1}\ln(e^x - 1)\,dx$

calculus integration special-functions definite-integrals riemann-zeta

Roots of Legendre Polynomial

real-analysis roots special-functions orthogonal-polynomials legendre-polynomials

How to solve $\int_0^\infty J_0(x)\ \text{sinc}(\pi\,x)\ e^{-x}\,\mathrm dx$?

special-functions definite-integrals improper-integrals closed-form

What is a closed form of $\int_0^1\ln(-\ln x)\ \text{li}\ x\ dx$

special-functions logarithms definite-integrals improper-integrals closed-form

A closed form for $\int_0^\infty\frac{e^{-x}\ J_0(x)\ \sin\left(x\,\sqrt[3]{2}\right)}{x}dx$

calculus integration special-functions definite-integrals closed-form

A closed-form expression for the integral $\int_0^\infty\text{Ci}^{3}(x) \, \mathrm dx$

calculus integration definite-integrals special-functions closed-form

What is the exact value of $\eta(6i)$?

special-functions gamma-function modular-forms

Limit of Zeta function

limits special-functions riemann-zeta euler-mascheroni-constant

Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$

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

Integral that arises from the derivation of Kummer's Fourier expansion of $\ln{\Gamma(x)}$

integration special-functions fourier-series gamma-function

Evaluating $\int_0^1 \frac{x \arctan x \log \left( 1-x^2\right)}{1+x^2}dx$

integration analysis definite-integrals special-functions

How to come up with the gamma function?

special-functions intuition gamma-function

What is $\lim\limits_{n\to\infty} (\text j_{x,x}-\text y_{x,x})$ with the BesselYZero and BesselJZero function?

limits roots special-functions bessel-functions constants

Simpler closed form for $\sum_{n=1}^\infty\frac{\Gamma\left(n+\frac{1}{2}\right)}{(2n+1)^4\,4^n\,n!}$

calculus sequences-and-series special-functions closed-form hypergeometric-function

Divergence of the Derivative of the Prime Counting Function

derivatives prime-numbers special-functions analytic-number-theory

Is there a closed form for this sum?

integration summation definite-integrals special-functions

Exponential integral $ \int_0^\infty \frac{x^t}{\Gamma(t+1)}\text dt$

real-analysis integration improper-integrals special-functions integral-transforms

Does $\left(n^2 \sin n\right)$ have a convergent subsequence?

sequences-and-series analysis special-functions