proof of recursion
- To: mathgroup at smc.vnet.net
- Subject: [mg112244] proof of recursion
- From: Magdalena Moczydlowska <magdamoczydlowska at gmail.com>
- Date: Mon, 6 Sep 2010 04:15:53 -0400 (EDT)
Good evening!
I have a big problem with proving the equivalence of two formulas. I
tried an induction but without success :
1) S_{m}(z)=(1/z)* \sum_{k=0}^{m-1} ( S_{k}(z)/(m-k)) where S_{0}
(z)=S(z)/z
2) S_{m}(z)=S(z)/(m!z^{m+1}) \sum _{k=1}^{m} (k! S(m,k) z^{m-k})
where S(m,k) is a Stirling number of a first type.
I will be grateful for your suggestion.
Magda