List questions from q-series | MathQa

Generalizations of the pentagonal number theorem

Published on 13 Jan 2025 - 2:08

How to prove that $\sum_{i=0}^n\frac{(a;q)_i}{(q;q)_i}\frac{(b;q)_{n-i}}{(q;q)_{n-i}}a^{n-i}=\frac{(ab;q)_n}{(q;q)_n}$?

Published on 13 Jan 2025 - 2:22

a conjecture of two equivalent q-continued fractions related to the reciprocal of the Göllnitz-Gordon continued fraction A111374-OEIS

Published on 12 Jan 2025 - 23:41

Closed form of the integral ${\large\int}_0^\infty e^{-x}\prod_{n=1}^\infty\left(1-e^{-24\!\;n\!\;x}\right)dx$

Published on 13 Jan 2025 - 2:08

Why $e^{\pi}-\pi \approx 20$, and $e^{2\pi}-24 \approx 2^9$?

Published on 13 Jan 2025 - 2:28

Weighted Q-binomial Coefficients

Published on 13 Jan 2025 - 2:08

show $\sum_{j=0}^n (-1)^j {n \brack j}_q =0$ for n odd

Published on 13 Jan 2025 - 2:16

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

Published on 13 Jan 2025 - 2:25

Reference request: $q$-gamma, $q$-polygamma, $q$-Pochhammer.

Published on 13 Jan 2025 - 2:23

how to prove these formulas about infinite product?

Published on 13 Jan 2025 - 2:11