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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


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