0
$\begingroup$

I'm currently struggling with ordinary generating functions(OGF) and was hoping somebody could point me in the direction of determining the OGF for the Stirling numbers of the second kind $\sum_{n=k}^\infty S(n,k) x^n$.

$\endgroup$
  • 2
    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ – Austin Mohr May 5 '13 at 16:44
  • $\begingroup$ That's a perfect link for the OGF but I'm having problems with proving that it's the OGf not just what the OGF is. $\endgroup$ – Atom May 5 '13 at 16:48
1
$\begingroup$

Take a look at Wilf's "generatingfunctionology". There you'll learn much of what there is about generating functions. A next step could be Flajolet and Sedgewick's "Analytic combinatorics" (careful, that one is quite a bit heavier going).

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ You can also read this post on how to apply a Norlund-Rice (contour) integral to a known identity for the Stirling numbers of the second kind to arrive at the same OGF. $\endgroup$ – mds May 30 '18 at 23:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.