New posts in Theta Functions

Summation of $\sum_{n=0}^{\infty}a^nq^{n^2}$

Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$

How are the Jacobi Theta Functions analogous to the Exponential Function?

An interesting identity involving Jacobi $\theta_4$ and $\zeta(2)$

How to evaluate sums in the form $\sum_{k=-\infty}^\infty e^{-\pi n k^2}$

Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$

Closed-form of an integral involving a Jacobi theta function, $ \int_0^{\infty} \frac{\theta_4^{n}\left(e^{-\pi x}\right)}{1+x^2} dx $

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

A $q$-continued fraction connected to the divisor function?

Ramanujan theta function and its continued fraction