Two remarkable doubly exponential series transformations of Ramanujan
type: Item
instance of: scholarly article
title: Two remarkable doubly exponential series transformations of Ramanujan
zbMATH Open document ID: 0798.33013
DOI: 10.1007/BF02830888
author: Bruce C. Berndt
author: James Lee Hafner
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1994-10-31T00:00:00Z
review text: The paper deals with two transformation formulas for double exponential series, as e.g. \[ \alpha \sum_{k=0}^ \infty \exp (-ne^{k\alpha}), \] which can be found in Ramanujan's second note book. The authors remark that the formulas there are of asymptotic nature only and give exact identities which are proven using Poisson's summation formula as the main tool.
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 562817
zbMATH Keywords: transformation formula
zbMATH Keywords: Gamma function
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: double exponential series
zbMATH Keywords: Poisson's summation
reviewed by: Ulrich Stadtmüller
MaRDI profile type: Publication
cites work: Q3218192
cites work: Q5513003
full work available at URL: https://doi.org/10.1007/bf02830888
OpenAlex ID: W1973159255
description: scientific article; zbMATH DE number 562817