On the identities of Ramanujan -- a \(q\)-series approach (Q6542686)
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scientific article; zbMATH DE number 7852197
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the identities of Ramanujan -- a \(q\)-series approach |
scientific article; zbMATH DE number 7852197 |
Statements
On the identities of Ramanujan -- a \(q\)-series approach (English)
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22 May 2024
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The author gives simple proofs of two identities of \textit{S. Ramanujan} [The Lost Notebook and other unpublished papers. With an introduction by George E. Andrews. New Delhi: Narosa Publishing House; Berlin (FRG): Springer-Verlag (1988; Zbl 0639.01023)]. \NThe first identity is:\N\[\sum^{\infty}_{n=0}\frac{(q; q^2)^2_n}{(-q; q)_{2n+1}}q^n=\sum^{\infty}_ {n=0}(-1)^nq^{n(n+1)}.\]\NThe second reads: \N\[\sum^\infty_ {n=0} \frac{(q;-q)_n} {(-q; q)_{2n+1}} q^n = \sum^\infty_ {n=0} (-1)^nq^{2n(n+1)}.\]
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theta functions
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false theta functions
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\(q\)-hypergeometric series
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