On Ramanujan's continued fraction for (q2;q3) ∞(q; q3)∞

George E. Andrews; Bruce C. Berndt; Jaebum Sohn; Ae Ja Yee; Alexandru Zaharescu

doi:10.1090/S0002-9947-02-03155-0

On Ramanujan's continued fraction for (q²;q³)_∞(q; q³)_∞

George E. Andrews
, Bruce C. Berndt
, Jaebum Sohn
, Ae Ja Yee
, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The continued fraction in the title is perhaps the deepest of Ramanujan's q-continued fractions. We give a new proof of this continued fraction, more elementary and shorter than the only known proof by Andrews, Berndt, Jacobsen, and Lamphere. On page 45 in his lost notebook, Ramanujan states an asymptotic formula for a continued fraction generalizing that in the title. The second main goal of this paper is to prove this asymptotic formula.

Original language	English (US)
Pages (from-to)	2397-2411
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	355
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9947-02-03155-0
State	Published - Jun 2003

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-02-03155-0

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AU - Zaharescu, Alexandru

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On Ramanujan's continued fraction for (q²;q³)_∞(q; q³)_∞

Abstract

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