Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

An identity for $(-q^{5};\,q^{10})_{\infty}$ (2111.11857v1)

Published 21 Nov 2021 in math.GM

Abstract: We prove that $$ \prod_{n=0}{\infty}(1+q{10n+5}) = \frac{\sum_{n=-\infty}{\infty}q{n{2}}\, \sum_{n=-\infty}{\infty}(-1){n}\, (-q){n(3n-1)/2}}{4\, \sum_{n\geq 0}(-q){\frac{n(n+1)}{2}}\sin \left{\frac{(2n+1)3\pi}{10}\right}\, \sum_{n\geq 0}(-q){\frac{n(n+1)}{2}}\sin \left{\frac{(2n+1)\pi}{10}\right}} \qquad |q|<1 $$ using identities due to Ramanujan.

Summary

We haven't generated a summary for this paper yet.