Mott Polynomial

Author

Eric W. Weisstein
November 21, 2008

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

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

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

Definition

ShefferS[n_,x_]:=n!SeriesCoefficient[Exp[((x(1-(Sqrt[1+(t^2)])))/t)],{t,0,n}]

Generating Function

SeriesCoefficient[Exp[(((1-(Sqrt[1+(t^2)])))/t)],{t,0,n}]

SeriesCoefficient[Exp[((x(1-(Sqrt[1+(t^2)])))/t)],{t,0,n}]

Together/@Series[Exp[((x(1-(Sqrt[1+(t^2)])))/t)],{t,0,5}]

With[{n=7},2^Range[0,n]Factorial[Range[0,n]]CoefficientList[CoefficientList[Series[Exp[((x(1-(Sqrt[1+(t^2)])))/t)],{t,0,n}],t],x]]//Column

Table

ShefferS[#,x]&/@Range[0,6]//Factor//Column//TraditionalForm

FindPolynomialRecurrence[ShefferS[#,x]&/@Range[0,10],4]

FindLinearRecurrence[ShefferS[#,x]&/@Range[6]]