## 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, - 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**
—, - Hari Ballabh Mittal,
*Some generating functions*, Univ. Lisboa Rev. Fac. Ci. A (2)**13**(1969/70), 43–54. MR**308486**
—, - 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, - 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

*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.

*Operational formulae for polynomials defined by a generalized Rodrigues formula*, (to appear).

*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.

*On pseudo Laguerre polynomials*, Michigan Thesis, 1953.

## 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