Rogers-Ramanujan type identities via Abel's lemma on summation by parts (Q2422046)
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| English | Rogers-Ramanujan type identities via Abel's lemma on summation by parts |
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Rogers-Ramanujan type identities via Abel's lemma on summation by parts (English)
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18 June 2019
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Many identities of the form \[ \text{infinite }q\text{-series = infinite }q\text{-product} \] arise in the theory of integer partitions and are known as Rogers-Ramanujan type identities. In this paper, the author considers the modified Abel's lemma on summation by parts [\textit{W. Chu}, Adv. Appl. Math. 39, No. 4, 490--514 (2007; Zbl 1131.33008)] in order to review and derive several Rogers-Ramanujan type identities.
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Rogers-Ramanujan identities
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basic hypergeometric series
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Abel's lemma on summation by parts
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