Newbetuts

Show that $\prod\limits_{n=1}^\infty \frac{(1-q^{6n})(1-q^n)^2}{(1-q^{3n})(1-q^{2n})}=\sum\limits_{n=-\infty}^\infty q^{2n^2+n}-3q^{9(2n^2+n)+1}$.

Extension of the Jacobi triple product identity

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

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 $

the ratio of jacobi theta functions and a new conjectured q-continued fraction

Combinatorial interpretation of this identity of Gauss?

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

Hermite's solution of the general quintic in terms of theta functions

Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$

What is a Theta Function?

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

Convexity of $\theta(q)$

A problem posed by Ramanujan involving $\sum e^{-5\pi n^2}$

Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$

Ramanujan theta function and its continued fraction

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

series involving $\log \left(\tanh\frac{\pi k}{2} \right)$

New posts in theta-functions

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

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

How many integer pairs satisfy the ellipse $x^2+ay^2=r?$

Show that $\prod\limits_{n=1}^\infty \frac{(1-q^{6n})(1-q^n)^2}{(1-q^{3n})(1-q^{2n})}=\sum\limits_{n=-\infty}^\infty q^{2n^2+n}-3q^{9(2n^2+n)+1}$.

Extension of the Jacobi triple product identity

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

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 $

the ratio of jacobi theta functions and a new conjectured q-continued fraction

Combinatorial interpretation of this identity of Gauss?

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

Hermite's solution of the general quintic in terms of theta functions

Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$

What is a Theta Function?

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

Convexity of $\theta(q)$

A problem posed by Ramanujan involving $\sum e^{-5\pi n^2}$

Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$

Ramanujan theta function and its continued fraction

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

series involving $\log \left(\tanh\frac{\pi k}{2} \right)$