Automatic Proof of Theta-Function Identities
Abstract
This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find theta-function identities as well as prove them. As an application, we show how to find and prove Ramanujan's 40 identities for his so called Rogers-Ramanujan functions G(q) and H(q). In his thesis Robins found similar identities for higher level generalized eta-products. Our ramarobinsids package is for finding and proving identities for generalizations of Ramanujan's G(q) and H(q) and Robin's extensions. These generalizations are associated with certain real Dirichlet characters. We find a total of over 150 identities.
Keywords
Cite
@article{arxiv.1807.08051,
title = {Automatic Proof of Theta-Function Identities},
author = {Jie Frye and Frank Garvan},
journal= {arXiv preprint arXiv:1807.08051},
year = {2018}
}
Comments
60 pages. See qseries.org/fgarvan/paper-supplements/auto-theta for supplements including MAPLE worksheets