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A new class of generating functions for hypergeometric polynomials.


Author: David Zeitlin
Journal: Proc. Amer. Math. Soc. 25 (1970), 405-412
MSC: Primary 33.20
DOI: https://doi.org/10.1090/S0002-9939-1970-0264123-3
MathSciNet review: 0264123
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Abstract: A new class of generating functions for generalized hypergeometric polynomials is obtained. Applications are given for the classical polynomials containing parameters, such as Jacobi, ultraspherical, and Laguerre polynomials, as well as for Hermite and Bessel polynomials. Two classes of generating functions recently obtained by J. W. Brown are discussed for independence.


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

  • [1] W. A. Al-Salam, The Bessel polynomials, Duke Math. J. 24 (1957), 529-545. MR 19, 849. MR 0090673 (19:849f)
  • [2] J. W. Brown, New generating functions for classical polynomials, Notices Amer. Math. Soc. 16 (1969), 412. Abstract #69T-B29. MR 0236438 (38:4734)
  • [3] -, New generating functions for classical polynomials, Proc. Amer. Math. Soc. 21 (1969), 263-268. MR 38 #4734. MR 0236438 (38:4734)
  • [4] L. Carlitz, Some generating functions for Laguerre polynomials, Duke Math. J. 35 (1968), 825-828. MR 0240351 (39:1700)
  • [5] H. W. Gould, Some generalizations of Vandermonde's convolution, Amer. Math. Monthly 63 (1956), 84-91. MR 17, 702. MR 0075170 (17:702g)
  • [6] -, A series transformation for finding convolution identities, Duke Math. J. 28 (1961), 193-202. MR 23 #A1216. MR 0123895 (23:A1216)
  • [7] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Vol. I, 3rd ed., Die Grundlehren der math. Wissenschaften, Bände 19, 20, Springer-Verlag, Berlin and New York, 1964. MR 30 #1219 a,b.
  • [8] J. Riordan, Combinatorial identities, Wiley, New York, 1968. MR 38 #53. MR 0231725 (38:53)
  • [9] H. M. Srivastava, A class of generating functions for generalized hypergeometric polynomials, Notices Amer. Math. Soc. 16 (1969), 975. Abstract #69T-B198.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0264123-3
Keywords: Generating functions, generalized hypergeometric polynomials, Jacobi polynomials, ultraspherical polynomials, Laguerre polynomials, Bessel polynomials, Hermite polynomials
Article copyright: © Copyright 1970 American Mathematical Society

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