Currently in the book on p. 19 (Neural Networks and Learning Machines Third Edition) I see:

Using the binomial expansion for $(1 - wz^{-1})^{-1}$ , we may rewrite it as $\sum_{l=0}^{\infty}w^{l}z^{-l}$. How Simon did that?


I suppose, that progression is connected to this rewriting. Hence, first formula is just the sum of an infinite decreasing geometric progression with $1$ as $b_{1}$ and $wz^{-1}$ as q.

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  • $\begingroup$ I think so too, but why he needs "binomial expansion" here?! $\endgroup$ – Marat Zakirov Sep 21 '15 at 10:57
  • $\begingroup$ okay, i'm not sure i did quite understand your question was. $\endgroup$ – dshulgin Sep 21 '15 at 11:00
  • $\begingroup$ maybe it's just expression to show a way of thinking. $\endgroup$ – dshulgin Sep 21 '15 at 11:02
  • $\begingroup$ You are correctly understood my question. $\endgroup$ – Marat Zakirov Sep 21 '15 at 11:05

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