Mixing
Double sum of Lambert series: Partial sum in closed form desired!
$begingroup$
We desire the things stated in the title for:
$sum_{k=2}^m sum_{n=1}^{k-1} {q^nover {1-q^n}}$
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.
Answer #2 from this other question, which may be able to help using theta functions
If you're going to jump into using Mathematica or Sage, check out the q-polygamma functions, specifically q-digamma
More on the q-digamma function, check out Wolfram Alpha's entry too
sequences-and-series theta-functions q-series q-analogs
asked Jan 21 at 5:25
user3108815user3108815
468
$endgroup$
add a comment |
$begingroup$
We desire the things stated in the title for:
$sum_{k=2}^m sum_{n=1}^{k-1} {q^nover {1-q^n}}$
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.
Answer #2 from this other question, which may be able to help using theta functions
If you're going to jump into using Mathematica or Sage, check out the q-polygamma functions, specifically q-digamma
More on the q-digamma function, check out Wolfram Alpha's entry too
sequences-and-series theta-functions q-series q-analogs
asked Jan 21 at 5:25
user3108815user3108815
468
$endgroup$
add a comment |
$begingroup$
We desire the things stated in the title for:
$sum_{k=2}^m sum_{n=1}^{k-1} {q^nover {1-q^n}}$
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.
Answer #2 from this other question, which may be able to help using theta functions
If you're going to jump into using Mathematica or Sage, check out the q-polygamma functions, specifically q-digamma
More on the q-digamma function, check out Wolfram Alpha's entry too
sequences-and-series theta-functions q-series q-analogs
asked Jan 21 at 5:25
user3108815user3108815
468
$endgroup$
We desire the things stated in the title for:
$sum_{k=2}^m sum_{n=1}^{k-1} {q^nover {1-q^n}}$
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.
Answer #2 from this other question, which may be able to help using theta functions
If you're going to jump into using Mathematica or Sage, check out the q-polygamma functions, specifically q-digamma
More on the q-digamma function, check out Wolfram Alpha's entry too
sequences-and-series theta-functions q-series q-analogs
sequences-and-series theta-functions q-series q-analogs
asked Jan 21 at 5:25
user3108815user3108815
468
asked Jan 21 at 5:25
user3108815user3108815
468
edited Jan 21 at 5:43
user3108815
asked Jan 21 at 5:25
user3108815user3108815
468
asked Jan 21 at 5:25
user3108815user3108815
468
asked Jan 21 at 5:25
user3108815user3108815
468
468
add a comment |
add a comment |
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