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 general sums kobi_78 Junior Fellow Posts: 11 Threads: 3 Joined: Dec 2009 06/24/2010, 07:56 PM Hi, I discovered it myself To derive it, use the rule that the multiplication of two power series is the discrete convolution of their coefficients and that $(1 - x)^{-1} = \sum_{n=0}^{\infty}{x^n}$. Now try to multiply a formal power series with $(1 - x)^{-1} = \sum_{n=0}^{\infty}{x^n}$. Repeat it k times and use the formula of $(1 - x)^{-k}$ to derive the formula. It however reminds Cauchy's formula for repeated integration (with all umbral calculus variations). « Next Oldest | Next Newest »

 Messages In This Thread general sums - by tommy1729 - 06/22/2010, 10:29 PM RE: general sums - by mike3 - 06/23/2010, 01:16 AM RE: general sums - by tommy1729 - 06/23/2010, 04:26 PM RE: general sums - by kobi_78 - 06/24/2010, 06:53 PM RE: general sums - by tommy1729 - 06/24/2010, 07:45 PM RE: general sums - by kobi_78 - 06/24/2010, 07:56 PM

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