Note on a continued fraction of Ramanujan (Q1567055)
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scientific article; zbMATH DE number 1455273
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on a continued fraction of Ramanujan |
scientific article; zbMATH DE number 1455273 |
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Note on a continued fraction of Ramanujan (English)
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5 June 2000
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In this note, making use of a Nörlund's continued fraction [see \textit{L. Lorentzen} and \textit{H. Waadeland}, Continued fractions with applications (1992; Zbl 0782.40001): p. 304, Theorem 2] as well as a hypergeometric formula due to S. Ramanujan [Notebooks (Vols. I, II), Tata Institute of Fundamental Research, Bombay (1957; Zbl 0138.24201): Notebook II; chapter 10, Corollary to Entry 34], a new proof of a certain continued fraction by Ramanujan involving a quotient of gamma function products [Notebook II, Chapter 12, Entry 25], is given. Other different proofs have been previously carried out by several authors.
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hypergeometric series
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Ramanujan
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hypergeometric differential equation
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continued fraction
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gamma function
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