New posts in zeta-functions

A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)

sequences-and-series alternative-proof zeta-functions

Riemann Zeta function - number of zeros

riemann-zeta zeta-functions

Show that $\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + 58 n^2} = - \frac{\pi \ln( 27 + 5 \sqrt {29})}{\sqrt {58}} $

sequences-and-series algebraic-number-theory zeta-functions

Factorial of infinity

factorial riemann-zeta zeta-functions

What is a zeta function?

analytic-number-theory riemann-zeta zeta-functions big-picture

Evaluating $\lim_{n\to\infty}\frac{1}{n+1}(\omega+\nu)^{(n+1)}z^\nu{_2F_1}(1,\omega+\nu+1;n+2;1-z)$

sequences-and-series gamma-function hypergeometric-function zeta-functions stirling-numbers

Does the Zeta Distribution converge to normal as N gets large

statistics normal-distribution central-limit-theorem zeta-functions

Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$

integration definite-integrals closed-form zeta-functions polylogarithm

What is the binomial sum $\sum_{n=1}^\infty \frac{1}{n^5\,\binom {2n}n}$ in terms of zeta functions?

special-functions binomial-coefficients analytic-number-theory riemann-zeta zeta-functions

Why does the $\sum_{n>1}(\zeta(n)-1)=1?$

number-theory zeta-functions

Does $\zeta(3)$ have a connection with $\pi$?

sequences-and-series analysis pi riemann-zeta zeta-functions

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^32^n}$

real-analysis sequences-and-series closed-form harmonic-numbers zeta-functions

Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function

integration special-functions gamma-function riemann-zeta zeta-functions

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

real-analysis sequences-and-series closed-form zeta-functions harmonic-numbers

How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?

real-analysis sequences-and-series complex-analysis zeta-functions

Gross-Zagier formulae outside of number theory

number-theory riemannian-geometry elliptic-curves homology-cohomology zeta-functions

Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$

integration sequences-and-series closed-form zeta-functions polylogarithm

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

analysis integration definite-integrals closed-form zeta-functions