Meixner Polynomial of the First Kind

Author

Eric W. Weisstein
November 29, 2008

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

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

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

Code

MeixnerM1[n_,x_,γ_,μ_]:=Pochhammer[γ,n]Hypergeometric2F1[-n,-x,γ,1-(μ^(-1))]

Generating Function

Sum[((MeixnerM1[k,x,b,c])/(k!))(t^k),{k,0,∞}]

FullSimplify[SeriesCoefficient[(((1-(t/c)))^x)(((1-t))^(-x-b)),{t,0,k}],k≥0&&k∈Integers]

Table

Table[MeixnerM1[n,x,b,c],{n,0,2}]//Simplify//Column//TraditionalForm