On a symmetric identity of Ramanujan involving the sum of two squares function

In his paper “On the expression of a number as the sum of two squares”, G.H. Hardy recorded a beautiful identity of Ramanujan, as well as its generalization, and described briefly their proofs. In this article, we give full details of Hardy's (and very likely Ramanujan's) proofs and presen...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-05, Vol.473 (2), p.1234-1243
Main Authors: Chan, Heng Huat, Toh, Pee Choon
Format: Article
Language:English
Subjects:
Bessel functions
Bessel polynomials
Sums of squares
Transformation formula
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Summary:In his paper “On the expression of a number as the sum of two squares”, G.H. Hardy recorded a beautiful identity of Ramanujan, as well as its generalization, and described briefly their proofs. In this article, we give full details of Hardy's (and very likely Ramanujan's) proofs and present some generalizations of Ramanujan's identity.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.01.018