Newbetuts

Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$

What is a geometric, physical or other meaning of the tetration?

Evaluation of an integral involving the Lambert W function

Yet another example of linear second order ODEs being reduced to hypergeometric functions.

Integral involving hypergeometric function $\int_0^1[{}_2F_1(\frac13,\frac23;1;x^3)]^2dx$

How to prove error function $\mbox{erf}$ is entire (i.e., analytic everywhere)?

Are there well known lower bounds for the upper incomplete gamma function?

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Fundamental solution for Helmholtz equation in higher dimensions

Can I express this sum as product of two theta functions?

what is exactly analytic continuation of the product log function

Why $p$-adically interpolate?

Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$

Erroneous numerical approximations of $\zeta\left(\frac{1}{2}\right)$?

Series expansion of incomplete gamma function ratio

Evaluate or simplify $\int\frac{1}{\ln x}\,dx$

Solving quintic equations of the form $x^5-x+A=0$

New posts in special-functions

Evaluating $\int_0^1 \frac{1}{\sqrt{\Gamma(x)}} dx$

Difficult infinite integral involving a Gaussian, Bessel function and complex singularities

Some interesting integrals with dilogarithm

Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$

What is a geometric, physical or other meaning of the tetration?

Evaluation of an integral involving the Lambert W function

Yet another example of linear second order ODEs being reduced to hypergeometric functions.

Integral involving hypergeometric function $\int_0^1[{}_2F_1(\frac13,\frac23;1;x^3)]^2dx$

How to prove error function $\mbox{erf}$ is entire (i.e., analytic everywhere)?

Are there well known lower bounds for the upper incomplete gamma function?

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Fundamental solution for Helmholtz equation in higher dimensions

Can I express this sum as product of two theta functions?

what is exactly analytic continuation of the product log function

Why $p$-adically interpolate?

Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$

Erroneous numerical approximations of $\zeta\left(\frac{1}{2}\right)$?

Series expansion of incomplete gamma function ratio

Evaluate or simplify $\int\frac{1}{\ln x}\,dx$

Solving quintic equations of the form $x^5-x+A=0$