Eikonal Blog

2010.01.04

Binomial symbol

Filed under: mathematics — Tags: , , — sandokan65 @ 19:56
  • Binomial theorem: (1-t)^{-\rho} = \sum_{n=0}^\infty \frac{\Gamma(\rho+n)}{\Gamma(\rho)}\frac{t^n}{n!}
    • “Source: The Functions of Mathematical Physics” by Harry Hochstadt
  • \sum_{r=0}^m(-)^r \binom{n}{r} = (-)^n \binom{n-1}{m} for 0 \le m \le n-1.
  • \sum_{r=k+1}^n (-)^{n-r} \binom{n}{r} = (-)^{n-k-1} \binom{n-1}{k}.

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