Newbetuts

Closed form of $\lim\limits_{n\to\infty}\left(\int_0^{n}\frac{{\rm d}k}{\sqrt{k}}-\sum_{k=1}^n\frac1{\sqrt k}\right)$

Integral in $n-$dimensional euclidean space

Infinite sum of Bessel Functions

Solving $(t^2+1)(y''-2y+1)=e^t$ with the initial conditions: $y(0)=y'(0)=1$

A tough series related with a hypergeometric function with quarter integer parameters

An infinite series expansion in terms of the polylogarithm function

Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

Integral with spherical symmetry over cube

Contour integration with branch points inside the contour.

How to evaluate the integral $\int_0^{2\pi} \theta\exp(x\cos(\theta) + y\sin(\theta))) d\theta$

Integral $I=\int_0^\infty \frac{\ln(1+x) \operatorname{Li}_2 (-x)}{x^{3/2}} dx$

About the integral $\int_{0}^{1}\text{arctanh}(x)\arcsin(x)\frac{dx}{x}$

A peculiar Euler sum

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

New posts in special-functions

How does one solve for $x$ in the equality $a^x = bx + c$?

Turning an elliptic curve over C into a complex torus

The Laurent series of the digamma function at the negative integers

How to integrate the dilogarithms?

Integral ${\large\int}_0^\infty\big(2J_0(2x)^2+2Y_0(2x)^2-J_0(x)^2-Y_0(x)^2\big)\,dx$

Prove $\int_{0}^{1} \frac{\sin^{-1}(x)}{x} dx = \frac{\pi}{2}\ln2$

Closed form of $\lim\limits_{n\to\infty}\left(\int_0^{n}\frac{{\rm d}k}{\sqrt{k}}-\sum_{k=1}^n\frac1{\sqrt k}\right)$

Integral in $n-$dimensional euclidean space

Infinite sum of Bessel Functions

Solving $(t^2+1)(y''-2y+1)=e^t$ with the initial conditions: $y(0)=y'(0)=1$

A tough series related with a hypergeometric function with quarter integer parameters

An infinite series expansion in terms of the polylogarithm function

Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

Integral with spherical symmetry over cube

Contour integration with branch points inside the contour.

How to evaluate the integral $\int_0^{2\pi} \theta\exp(x\cos(\theta) + y\sin(\theta))) d\theta$

Integral $I=\int_0^\infty \frac{\ln(1+x) \operatorname{Li}_2 (-x)}{x^{3/2}} dx$

About the integral $\int_{0}^{1}\text{arctanh}(x)\arcsin(x)\frac{dx}{x}$

A peculiar Euler sum

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $