Generalizations of Rogers–Ramanujan type identities Generalizations of Rogers–Ramanujan type identities

The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this pap...

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Bibliographic Details
Published in:The Ramanujan journal Vol. 68; no. 1; p. 32
Main Authors: Cui, Su-Ping, Gu, Nancy S. S., Wang, Qian
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2025
Springer Nature B.V
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Bailey’s lemma
Bailey pairs
Appell–Lerch sums
11F27
Rogers–Ramanujan type identities
11P84
ISSN:1382-4090, 1572-9303
Online Access:Get full text
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Summary:The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this paper, by means of properties of Appell–Lerch sums in combination with Bailey pairs and Bailey’s lemma, we derive some generalizations of Rogers–Ramanujan type identities, which include some known identities and also imply some new ones.
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-025-01174-8