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Some classes of generating functions for the Laguerre and Hermite polynomials


Author: M. E. Cohen
Journal: Math. Comp. 31 (1977), 511-518
MSC: Primary 33A65
DOI: https://doi.org/10.1090/S0025-5718-1977-0442323-1
MathSciNet review: 0442323
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Abstract: In the first half of the article, we present two theorems which give, as special cases, a number of new classes of generating functions for the Laguerre polynomial. These formulae extend the recent results of Carlitz [2] and others. The latter part of our work deals with two theorems involving new generating functions for the Hermite and generalized Hermite polynomials, thus generalizing some well-known expansions. The method of proof adopted in this paper differs from that of previous workers.


References [Enhancements On Off] (What's this?)

  • [1] J. W. BROWN, "On zero type sets of Laguerre polynomials," Duke Math. J., v. 35, 1968, pp. 821-823. MR 38 #2348. MR 0234027 (38:2348)
  • [2] L. CARLITZ, "Some generating functions for Laguerre polynomials," Duke Math. J., v. 35, 1968, pp. 825-827. MR 39 #1700. MR 0240351 (39:1700)
  • [3] S. K. CHATTERJEA, "Some generating functions," Duke Math. J., v. 32, 1965, pp. 563-564. MR 31 #5989. MR 0181762 (31:5989)
  • [4] M. E. COHEN, "On expansion problems: New classes of formulas for the classical functions," SIAM J. Math. Anal, v. 7, 1976, pp. 702-712. MR 0442305 (56:691)
  • [5] M. E. COHEN, "Generating functions for the Jacobi polynomial," Proc. Amer. Math. Soc., v. 57, 1976, pp. 271-275. MR 0404725 (53:8525)
  • [6] A. ERDÉLYI et al., Higher Transcendental Functions, Vols. I, II, McGraw-Hill, New York, 1953. MR 15, 419. MR 0058756 (15:419i)
  • [7] H. W. GOULD & A. T. HOPPER, "Operational formulas connected with two generalizations of Hermite polynomials," Duke Math. J., v. 29, 1962, pp. 51-63. MR 24 #A2689. MR 0132853 (24:A2689)
  • [8] R. P. GUPTA & G. C. JAIN, "A generalized Hermite distribution and its properties," SIAM J. Appl. Math., v. 27, 1974, pp. 359-363. MR 50 #2580. MR 0350087 (50:2580)
  • [9] Y. L. LUKE, Mathematical Functions and Their Approximations, Academic Press, New York, 1975. MR 0501762 (58:19039)
  • [10] D. ZEITLIN, "A new class of generating functions for hypergeometric polynomials," Proc. Amer. Math. Soc., v. 25, 1970, pp. 405-412. MR 41 #8719. MR 0264123 (41:8719)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0442323-1
Keywords: Generating functions, Hermite polynomial, hypergeometric function, incomplete gamma function, Laguerre polynomial, operators
Article copyright: © Copyright 1977 American Mathematical Society

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