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An Identity Relating a Theta Function to a Sum of Lambert Series
Author(s) -
Andrews George E.,
Lewis Richard,
Liu ZhiGuo
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.1.25
Subject(s) - mathematics , ramanujan's sum , identity (music) , dirichlet series , series (stratigraphy) , pure mathematics , lambert w function , ramanujan theta function , function (biology) , theta function , dirichlet distribution , mathematical analysis , combinatorics , paleontology , evolutionary biology , biology , physics , acoustics , boundary value problem
We derive an identity connecting a theta function and a sum of Lambert series. As a consequence of this identity, we deduce a number of results of Jacobi, Dirichlet, Lorenz, Ramanujan and Rademacher.