New generating functions for hypergeometric polynomials. (English) Zbl 0573.33010
The authors obtain some linear generating functions for hypergeometric polynomials given by
\[
\nu_ n(x)=\sum^{n}_{k=0}(-1)^ kn!P_ k(x)/(k!)^ 2(n-k)!,
\]
derive, as special cases, generalizations of some known generating functions and also give a few generating functions in terms of double hypergeometric functions of Humbert and Horn.
Reviewer: K.M.Saksena
MSC:
33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
33C05 | Classical hypergeometric functions, \({}_2F_1\) |