I recently learned about the Stirling Numbers, and I'm trying to get my head around them. I understand that the 2nd Kind numbers are the coefficients that will convert a polynomial in the standard (monomial power) basis to the falling power basis. I found a piece on Planetmath that presents a proof of this, but I can't follow it.
There must be somebody out there who knows more about the Stirling Numbers than I do. I hope you can explain this proof to me, or tell me where the author went wrong, if that's the case.
Thanks in advance. I've attached two pdfs. One is the Planetmath piece, the other is by me an explains my difficulties (I hope).