Double sum of Lambert series: Partial sum in closed form desired!

Asked Jan 21 '19 at 05:25

Active Jan 21 '19 at 12:15

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We desire the things stated in the title for:

$\sum_{k=2}^m \sum_{n=1}^{k-1} {q^n\over {1-q^n}}$

Some things I've looked into that may be of some help:

The first sum is just a truncated (partially summed) Lambert series, so take a look at the truncated Lambert series.

edited Jan 21 '19 at 05:43

asked Jan 21 '19 at 05:25

user3108815

There are some interesting expansions towards this end in this article. – mds Jun 02 '19 at 17:52

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