Some combinatorial identities and arithmetical applications
type: Item
instance of: scholarly article
title: Some combinatorial identities and arithmetical applications
zbMATH Open document ID: 0585.10034
DOI: 10.1216/RMJ-1985-15-2-365
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author describes an elementary method of raising both members of the Jacobi triple-product identity to the second and fourth powers. For example, the second power becomes \[ \prod^{\infty}_{n=1}(1- x^{2n})^ 2\quad (1+a x^{2n-1})^ 2\quad (1+a^{-1} x^{2n-1})^ 2= \] \[ =\sum^{\infty}_{-\infty}x^{2n^ 2}\sum^{\infty}_{- \infty}x^{2n^ 2} a^{2n}+x\sum^{U}_{-\infty}x^{2n(n+1)}\quad \sum^{\infty}_{-\infty}x^{2n(n+1)} a^{2n+1}. \] Some arithmetical applications are also noted.
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 3937267
zbMATH Keywords: infinite products
zbMATH Keywords: power series identities
zbMATH Keywords: elementary method
zbMATH Keywords: Jacobi triple-product identity
zbMATH Keywords: fourth powers
zbMATH Keywords: second power
zbMATH Keywords: arithmetical applications
author: John A. Ewell
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-2-365
OpenAlex ID: W2093895469
description: scientific article; zbMATH DE number 3937267