Polynomials defined by generating relations
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- by Hari Ballabh Mittal PDF
- Trans. Amer. Math. Soc. 168 (1972), 73-84 Request permission
Abstract:
Various authors have made efforts for finding new generating functions for known polynomial sets. In the present paper, by making use of the operator ${T_k} = x(k + xD)$, a number of generating functions and characterizations have been obtained for various polynomials in a systematic manner.References
- W. A. Al-Salam, The Bessel polynomials, Duke Math. J. 24 (1957), 529–545. MR 90673
- Waleed A. Al-Salam, Some functions related to the Bessel polynomials, Duke Math. J. 26 (1959), 519–539. MR 109233 W. N. Bailey, Transformations of generalized hypergeometric series, Proc. London Math. Soc. 29 (1929), 495-502. P. E. Bedient, Polynomials related to Appell functions of two variables, Michigan Thesis, 1958.
- J. W. Brown, On Burchnall’s generating relation for Bessel polynomials, Amer. Math. Monthly 74 (1967), 1104–1107. MR 220982, DOI 10.2307/2313626
- J. W. Brown, On zero type sets of Laguerre polynomials, Duke Math. J. 35 (1968), 821–823. MR 234027, DOI 10.1215/S0012-7094-68-03586-2
- James Ward Brown, On the Sheffer $A$-type of certain modified polynomial sets, Proc. Amer. Math. Soc. 23 (1969), 718–722. MR 247151, DOI 10.1090/S0002-9939-1969-0247151-5
- L. Carlitz, Some generating functions for Laguerre polynomials, Duke Math. J. 35 (1968), 825–827. MR 240351
- S. K. Chatterjea, On a generalization of Laguerre polynomials, Rend. Sem. Mat. Univ. Padova 34 (1964), 180–190. MR 166421
- Mary Celine Fasenmyer, Some generalized hypergeometric polynomials, Bull. Amer. Math. Soc. 53 (1947), 806–812. MR 22276, DOI 10.1090/S0002-9904-1947-08893-5
- H. W. Gould and A. T. Hopper, Operational formulas connected with two generalizations of Hermite polynomials, Duke Math. J. 29 (1962), 51–63. MR 132853, DOI 10.1215/S0012-7094-62-02907-1
- H. L. Krall and Orrin Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100–115. MR 28473, DOI 10.1090/S0002-9947-1949-0028473-1
- H. B. Mittal, A generalization of the Laguerre polynomials, Publ. Math. Debrecen 18 (1971), 53–58 (1972). MR 310313
- Hari Ballabh Mittal, Operational representation for the generalized Laguerre polynomial, Glasnik Mat. Ser. III 6(26) (1971), 45–53 (English, with Serbo-Croatian summary). MR 299847 —, Operational formulae for polynomials defined by a generalized Rodrigues formula, (to appear).
- Hari Ballabh Mittal, Some generating functions, Univ. Lisboa Rev. Fac. Ci. A (2) 13 (1969/70), 43–54. MR 308486 —, On results involving generating functions and generalized hypergeometric function, Comment. Math. Univ. Carolinae (to appear). —, A study of certain generating functions and associated polynomial sets, Lucknow University Thesis, Lucknow, India, 1970. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Vol. 1, 3rd ed., Die Grundlehren der math. Wissenschaften, Band 19, Springer-Verlag, Berlin, 1964. MR 30 #1219a.
- E. D. Rainville, Generating functions for Bessel and related polynomials, Canad. J. Math. 5 (1953), 104–106. MR 54104, DOI 10.4153/cjm-1953-013-5
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725 R. L. Shively, On pseudo Laguerre polynomials, Michigan Thesis, 1953.
- Letterio Toscano, Funzioni generatrici di particolari polinomi di Laguerre e di altri da essi dipendenti, Boll. Un. Mat. Ital. (3) 7 (1952), 160–167 (Italian). MR 0050062
- Louis Weisner, Group-theoretic origin of certain generating functions, Pacific J. Math. 5 (1955), 1033–1039. MR 86905, DOI 10.2140/pjm.1955.5.1033
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 168 (1972), 73-84
- MSC: Primary 33A70
- DOI: https://doi.org/10.1090/S0002-9947-1972-0294743-8
- MathSciNet review: 0294743