On modular equations of degree 25

On page 237–238 of his second notebook, Ramanujan recorded five modular equations of composite degree 25. Berndt proved all these using the method of parametrization. He also expressed that his proofs undoubtedly often stray from the path followed by Ramanujan. The purpose of this paper is to give d...

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Bibliographic Details
Published in:The Ramanujan journal 2021-11, Vol.56 (2), p.743-752
Main Authors: Vasuki, K. R., Yathirajsharma, M. V.
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Parameterization
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Summary:On page 237–238 of his second notebook, Ramanujan recorded five modular equations of composite degree 25. Berndt proved all these using the method of parametrization. He also expressed that his proofs undoubtedly often stray from the path followed by Ramanujan. The purpose of this paper is to give direct proofs to four of the five modular equations using the identities known to Ramanujan.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00276-9