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<p>Ramanujan recorded five <i>q</i>-series identities at the end of his second notebook and an unified generalization of these identities was 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 analogues 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.</p>

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One variable generalizations of five entries of Ramanujan and their finite analogues

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Archit Agarwal

摘要

Ramanujan recorded five q-series identities at the end of his second notebook and an unified generalization of these identities was 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 analogues 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.