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Asymptotic Formulas for Two Continued Fractions in Ramanujan's Lost Notebook
Author(s) -
Berndt Bruce C.,
Sohn Jaebum
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002952
Subject(s) - ramanujan's sum , riemann zeta function , corollary , mathematics , dirichlet distribution , ramanujan tau function , ramanujan theta function , dirichlet series , riemann hypothesis , asymptotic formula , pure mathematics , combinatorics , mathematical analysis , boundary value problem
On page 45 of his lost notebook, Ramanujan recorded two asymptotic formulas for two continued fractions involving the Riemann zeta‐function and Dirichlet L ‐functions. The paper proves a more general theorem and derives Ramanujan's claims as a corollary of the theorem.