One variable Generalization of five entries of Ramanujan and their finite analogue

2024/10/17 by Archit Agarwal, Agarwal, Archit
Mathematics · #05A17 #33D15 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #Primary 11P81 #Secondary 11P84

paper · pdf · doi:10.48550/arxiv.2410.13430

openalex publication_date 2024/10/17 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28

Abstract

Ramanujan recorded five q-series identities at the end of his second notebook and an unified generalization of these identities obtained by Bhoria, Eyyunni and Maji. Recently, Dixit and Patel gave a finite analogue of the identity of Bhoria et. al. which in turn gives finite analogue of all the aforementioned identities of Ramanujan. In this paper, one of our main goals is to obtain a one-variable generalization of the identity of Bhoria et. al. along with its finite analogue, which naturally generalizes the result of Dixit and Patel. Utilizing these newly established identities, we derive one-variable generalizations for each of the five entries by Ramanujan and their corresponding finite analogues.

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