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Keywords:
Ultraspherical type generalization of Bateman’s polynomials; ultraspherical type generalization of Pasternak’s polynomials; Jacobi type generalization of Bateman’s polynomials; Jacobi type generalization of Pasternak’s polynomials. Sister Celine’s polynomial; Hahn polynomial; Generalized Hermite polynomial; Krawtchouk’s polynomial; Meixner’s polynomial; Charlier polynomial; Sylvester’s polynomial; Gottlieb’s polynomial; Konhauser’s polynomial; generating functions; integral relations
Ultraspherical type generalization of Bateman’s polynomials; ultraspherical type generalization of Pasternak’s polynomials; Jacobi type generalization of Bateman’s polynomials; Jacobi type generalization of Pasternak’s polynomials. Sister Celine’s polynomial; Hahn polynomial; Generalized Hermite polynomial; Krawtchouk’s polynomial; Meixner’s polynomial; Charlier polynomial; Sylvester’s polynomial; Gottlieb’s polynomial; Konhauser’s polynomial; generating functions; integral relations
Summary:
Certain generalizations of Sister Celine’s polynomials are given which include most of the known polynomials as their special cases. Besides, generating functions and integral representations of these generalized polynomials are derived and a relation between generalized Laguerre polynomials and generalized Bateman’s polynomials is established.
References:
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