New posts in special-functions

Elliptic integral $\int^1_0 \frac{K(k)}{\sqrt{1-k^2}}\,dk$

integration definite-integrals special-functions elliptic-integrals

Compute polylog of order $3$ at $\frac{1}{2}$

calculus integration sequences-and-series special-functions polylogarithm

Can this integral $\int_0^{2\pi} \frac{d\theta}{(a^2 \cos^2 \theta +b^2\sin^2\theta)^{3/2}}$ be written in the form of a elliptic integral

integration special-functions elliptic-integrals

Tough Inverse Fourier Transform

ordinary-differential-equations fourier-analysis special-functions definite-integrals closed-form

Integral Representation of Infinite series

combinatorics analysis special-functions generating-functions residue-calculus

The most complete reference for identities and special values for polylogarithm and polygamma functions

reference-request special-functions gamma-function polylogarithm polygamma

An integral involving a Gaussian, error functions and the Owen's T function.

integration special-functions error-function polylogarithm

Solve $-B \ln y -A y \ln y + A y- A =0$ for $y$

calculus special-functions logarithms gamma-function transcendental-equations

Closed-form of $\int_0^1 \left(\ln \Gamma(x)\right)^3\,dx$

calculus definite-integrals special-functions closed-form gamma-function

Elliptic functions as inverses of Elliptic integrals

complex-analysis special-functions elliptic-functions

An identity involving integrals of the form $\int_{0}^{\alpha} \arctan (\sqrt{5}\tan\theta) \, d\theta$.

integration definite-integrals special-functions

Is there a way to analytically solve $x^\alpha + y^\alpha = \alpha(x + y)$ for $\alpha$, other than $\alpha = 1$?

algebra-precalculus special-functions closed-form

Evaluate $\sum _{n=1}^{\infty } \frac{\sin \left(x \sqrt{a^2+n^2}\right)}{\left(a^2+n^2\right)^{3/2}}$ and generalize it

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

The log integrals $\int_{0}^{1/2} \frac{\log(1+2x) \log(x)}{1+x} \, dx $ and $ \int_{0}^{1/2} \frac{\log(1+2x) \log(1-x)}{1+x} \, dx$

definite-integrals special-functions polylogarithm

a conjectured continued-fraction for $\displaystyle\cot\left(\frac{z\pi}{4z+2n}\right)$ that leads to a new limit for $\pi$

number-theory special-functions gamma-function continued-fractions conjectures

Clausen and Riemann zeta function

real-analysis special-functions riemann-zeta

An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

integration contour-integration special-functions closed-form

How are Fox-H functions useful in math?

integration complex-analysis special-functions

Closed-form of $\int_0^1\left(\frac{\arctan x}{x}\right)^n\,dx$

calculus integration definite-integrals special-functions closed-form

Gamma function has no zeros

complex-analysis special-functions gamma-function