On computing the generalized Lambert series

Details On computing the generalized Lambert series On computing the generalized Lambert series

2012-02-29

arxiv.org/abs/1202.6525v2

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

We show how the generalized Lambert series sum(n>=1, x*q^n/(1-x*q^n)) can be computed with Theta convergence. This allows the computation of the sum of the inverse Fibonacci numbers without splitting the sum into even and odd part. The method is a special case of an expression for the more general series sum(n>=0, t^n/(1-x*q^n)), which can be obtained from either the Rogers-Fine identity or an identity by Osler and Hassen.

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