Previous |  Up |  Next


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
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.
[1] Chihara, T. S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York, London and Paris, 1978. MR 0481884 | Zbl 0389.33008
[2] Fasenmyer, Sister M. Celine: Some generalized hypergeometric polynomials. Bull. Amer. Math. Soc. 53 (1947), 806–812. DOI 10.1090/S0002-9904-1947-08893-5 | MR 0022276
[3] Khandekar, P. R.: On a generalization of Rice’s polynomial. I. Proc. Nat. Acad. Sci. India, Sect. A34 (1964), 157–162. MR 0219773 | Zbl 0166.32002
[4] Konhauser, J. D. E.: Some properties of biorthogonal polynomials. J. Math. Anal. Appl. 11 (1965), 242–260. DOI 10.1016/0022-247X(65)90085-5 | MR 0185167 | Zbl 0125.31501
[5] Konhauser, J. D. E.: Biorthogonal polynomials suggested by Laguerre polynomials. Pacific J. Math. 21 (1967), 303–314. DOI 10.2140/pjm.1967.21.303 | MR 0214825
[6] Rainville, E. D.: Special Functions. Macmillan, New York; Reprinted by Chelse Publ. Co., Bronx, New York, 1971. MR 0393590 | Zbl 0231.33001
[7] Srivastava, H. M. and Manocha, H. L.: A Treatise on Generating Functions. John Wiley and Sons (Halsted Press), New York; Ellis Horwood, Limited Chichester, 1984. MR 0750112
Partner of
EuDML logo