Power Polynomial

Author

Eric W. Weisstein
December 3, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/PowerPolynomial.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Sums

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

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

Generating Function

ExponentialGeneratingFunction[(x^n),n,t]

Series[(E^(t x)),{t,0,10}]

SeriesCoefficient[(E^(t x)),{t,0,n}]

GeneratingFunction[(x^n),n,t]

Series[(1/(1-t x)),{t,0,10}]

SeriesCoefficient[(1/(1-t x)),{t,0,n}]