Umbral Calculus

Author

Eric W. Weisstein
January 9, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/UmbralCalculus.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/UmbralCalculus.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Sums

(∑_(k=0)^n)(Pochhammer[a, k]) (Binomial[n, k]) (Pochhammer[x, n-k])==(Pochhammer[a+x, n])

Sum[Binomial[n,k]Pochhammer[a,k]Pochhammer[x,n-k],{k,0,n}]

FullSimplify[%]

FullSimplify[%-Pochhammer[x+a,n]]

(∑_(k=0)^n)(a^k) (Binomial[n, k]) (x^(n-k))==(((a+x))^n)

Sum[a^k*Binomial[n, k]*x^(n - k), {k, 0, n}]