Skip to main content
MathOverflow

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

6
  • $\begingroup$ Thank you very much for your answer! Is there an online platform where I can find identities such as the one you mentioned? Or is it just something one has to know from experience? $\endgroup$
    – Susp1cious
    Commented Nov 16, 2019 at 22:06
  • 5
    $\begingroup$ Wilf's generatingfunctionology and Graham, Knuth, et al.'s Concrete Mathematics are good sources for manipulating sums. $\endgroup$
    – RobPratt
    Commented Nov 16, 2019 at 23:26
  • $\begingroup$ My result for $a=2$ is slightly different. Is it possible that you forgot to eliminate the $2$ from the Binomial? Shouldn't the expression be $\sum_{k=0}^\infty b_{2k}=\sum_{k=0}^\infty\biggl(\frac{1}{2}\sum_{j=0}^1\exp(\pi\ ijk)\biggr)\frac{x^k}{k!}\sum_{l\geq0}\binom{k}{l}$ $\endgroup$
    – Susp1cious
    Commented Nov 17, 2019 at 8:57
  • $\begingroup$ @Susp1cious, why is the bottom of your binomial coefficient $\ell$ when it is independent of $k$? $\endgroup$
    – J. M. isn't a mathematician
    Commented Nov 17, 2019 at 15:08
  • $\begingroup$ No, I made a different error, which I should have noticed because evaluating at $x=0$ should yield 1. I’ll fix it. $\endgroup$
    – RobPratt
    Commented Nov 17, 2019 at 15:20