The polynomials 
which form the Sheffer
sequence for
 |  | ![{[1+deltaf(t)]^2+[f(t)]^2}^(eta/2)](/images/equations/MeixnerPolynomialoftheSecondKind/Inline4.svg) |
(1)
|
 |  |  |
(2)
|
which have generating function
![sum_(k=0)^infty(M_k(x;delta,eta))/(k!)t^k
=[(1+deltat)^2]^(-eta/2)exp((xtan^(-1)t)/(1-deltatan^(-1)t)).](/images/equations/MeixnerPolynomialoftheSecondKind/NumberedEquation1.svg) |
(3)
|
The first few are
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  | ![x^2+2delta(1-eta)x+eta[(eta+1)delta^2-1].](/images/equations/MeixnerPolynomialoftheSecondKind/Inline16.svg) |
(6)
|
Meixner Polynomial of the Second Kind
See also
Meixner Polynomial of the First Kind, Sheffer SequenceExplore with Wolfram|Alpha
References
Chihara, T. S. An Introduction to Orthogonal Polynomials. New York: Gordon and Breach, p. 179, 1978.Roman, S. The Umbral Calculus. New York: Academic Press, 1984.Referenced on Wolfram|Alpha
Meixner Polynomial of the Second KindCite this as:
Weisstein, Eric W. "Meixner Polynomial of the Second Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeixnerPolynomialoftheSecondKind.html