Geodesic
On some generalized Sister Celine’s polynomials
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 527-545 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 33C45
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 
@article{CMJ_1999_49_3_a6,
     author = {Khan, Mumtaz Ahmad and Shukla, Ajay Kumar},
     title = {On some generalized {Sister} {Celine{\textquoteright}s} polynomials},
     journal = {Czechoslovak Mathematical Journal},
     pages = {527--545},
     year = {1999},
     volume = {49},
     number = {3},
     mrnumber = {1708366},
     zbl = {1005.33002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a6/}
}
TY  - JOUR
AU  - Khan, Mumtaz Ahmad
AU  - Shukla, Ajay Kumar
TI  - On some generalized Sister Celine’s polynomials
JO  - Czechoslovak Mathematical Journal
PY  - 1999
SP  - 527
EP  - 545
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a6/
LA  - en
ID  - CMJ_1999_49_3_a6
ER  - 
%0 Journal Article
%A Khan, Mumtaz Ahmad
%A Shukla, Ajay Kumar
%T On some generalized Sister Celine’s polynomials
%J Czechoslovak Mathematical Journal
%D 1999
%P 527-545
%V 49
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a6/
%G en
%F CMJ_1999_49_3_a6
Khan, Mumtaz Ahmad; Shukla, Ajay Kumar. On some generalized Sister Celine’s polynomials. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 527-545. http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a6/

[1] Chihara, T. S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York, London and Paris, 1978. | MR | Zbl

[2] Fasenmyer, Sister M. Celine: Some generalized hypergeometric polynomials. Bull. Amer. Math. Soc. 53 (1947), 806–812. | DOI | MR

[3] Khandekar, P. R.: On a generalization of Rice’s polynomial. I. Proc. Nat. Acad. Sci. India, Sect. A34 (1964), 157–162. | MR | Zbl

[4] Konhauser, J. D. E.: Some properties of biorthogonal polynomials. J. Math. Anal. Appl. 11 (1965), 242–260. | DOI | MR | Zbl

[5] Konhauser, J. D. E.: Biorthogonal polynomials suggested by Laguerre polynomials. Pacific J. Math. 21 (1967), 303–314. | DOI | MR

[6] Rainville, E. D.: Special Functions. Macmillan, New York; Reprinted by Chelse Publ. Co., Bronx, New York, 1971. | MR | Zbl

[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