On the logarithmic derivative of a theta function and a fundamental identity of Ramanujan
type: Item
instance of: scholarly article
title: On the logarithmic derivative of a theta function and a fundamental identity of Ramanujan
zbMATH Open document ID: 0778.33002
author: Li-Chien Shen
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
review text: We derive a fundamental identity of Ramanujan from the identity \(\bigl( {{f'} \over f}\bigr)'= {{f''} \over f}- \bigl({{f'} \over f}\bigr)^ 2\); from this persective, this identity of Ramanujan becomes an analogue of the familiar trigonometric identity \(1+\cot^ 2\theta=\cos^ 2\theta\) and many quantities associated with this Ramanujan's identity can be seen as natural extensions of their trigonometric counterparts.
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 399111
zbMATH Keywords: theta functions
zbMATH Keywords: Eisenstein series
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1259
OpenAlex ID: W2011950643
DOI: 10.1006/JMAA.1993.1259
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description: scientific article; zbMATH DE number 399111