New posts in special-functions

Derive the recurrence relations

combinatorics recurrence-relations special-functions

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

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

Sum=Integral? Find $m$ so that $\sum _{n=1}^{\infty } \frac{n^m}{e^{2 \pi n}-1}=\int_0^{\infty } \frac{x^m}{e^{2 \pi x}-1} \, dx$

sequences-and-series definite-integrals special-functions

Prove $_2F_1\!\left(\frac76,\frac12;\,\frac13;\,-\phi^2\right)=0$

calculus special-functions hypergeometric-function golden-ratio

Rogers-Ramanujan continued fraction in terms of Jacobi theta functions?

special-functions modular-forms continued-fractions theta-functions

Proof of a dilogarithm identity

calculus special-functions closed-form polylogarithm

Integral of product of two error functions (erf)

integration special-functions

Is there a combinatorial way to see the link between the beta and gamma functions?

combinatorics special-functions binomial-coefficients gamma-function

More on the integral $\int_0^1\int_0^1\int_0^1\int_0^1\frac{1}{(1+x) (1+y) (1+z)(1+w) (1+ x y z w)} \ dx \ dy \ dz \ dw$

integration multivariable-calculus definite-integrals special-functions polylogarithm

A logarithmic integral, generalization of a result of Shalev

definite-integrals summation special-functions elliptic-integrals polylogarithm

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

integration ordinary-differential-equations definite-integrals special-functions

Expected value of $\ln X$ if $X$ is $\Gamma(a,b)$ distributed.

probability statistics special-functions

Evaluate $\int_{0}^{\frac {\pi}{3}}x\log(2\sin\frac {x}{2})\,dx$

calculus integration definite-integrals special-functions improper-integrals

Continuous function with local maxima everywhere but no global maxima

analysis continuity special-functions

An infinite product for $\left(\frac{\eta(13\tau)}{\eta(\tau)}\right)^2$?

special-functions modular-forms

Behaviour of the series $\exp_p(x)=\sum_{k=0}^{\infty}\frac{x^k}{(k!)^p}$ depending on $p\approx 2$?

sequences-and-series special-functions recreational-mathematics

Prove $f(x)=\int\frac{e^x}{x}\mathrm dx$ is not an elementary function

calculus integration special-functions

Reference Book on Special Functions

reference-request soft-question special-functions book-recommendation

How do I develop numerical routines for the evaluation of my own special functions?

numerical-methods special-functions computational-mathematics

How this integral $ \int_0^z\frac{1-e^x}{x} dx$ is connected to the Gamma function and Euler constant?

complex-analysis integration special-functions