On computing the generalized Lambert series
Classical Analysis and ODEs
2012-06-26 v3
Abstract
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.
Cite
@article{arxiv.1202.6525,
title = {On computing the generalized Lambert series},
author = {Jörg Arndt},
journal= {arXiv preprint arXiv:1202.6525},
year = {2012}
}
Comments
8 pages; now mentioned that identity (1) appears in a 1993 paper by R. P. Agarwal