Polynomial expansions
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- by Jerry L. Fields and Mourad E. H. Ismail PDF
- Math. Comp. 29 (1975), 894-902 Request permission
Abstract:
The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given.References
- Ralph P. Boas Jr. and R. Creighton Buck, Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 19, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin, 1964. Second printing, corrected. MR 0162914
- J. W. Brown, On zero type sets of Laguerre polynomials, Duke Math. J. 35 (1968), 821–823. MR 234027
- J. W. Brown, New generating functions for classical polynomials, Proc. Amer. Math. Soc. 21 (1969), 263–268. MR 236438, DOI 10.1090/S0002-9939-1969-0236438-8
- L. Carlitz, Some generating functions for Laguerre polynomials, Duke Math. J. 35 (1968), 825–827. MR 240351
- Jerry L. Fields and Jet Wimp, Expansions of hypergeometric functions in hypergeometric functions, Math. Comp. 15 (1961), 390–395. MR 125992, DOI 10.1090/S0025-5718-1961-0125992-3
- Jerry L. Fields and Jet Wimp, Basic series corresponding to a class of hypergeometric polynomials, Proc. Cambridge Philos. Soc. 59 (1963), 599–605. MR 150350
- Mourad El-Houssieny Ismail, On obtaining generating functions of Boas and Buck type for orthogonal polynomials, SIAM J. Math. Anal. 5 (1974), 202–208. MR 338484, DOI 10.1137/0505022 Y. L. LUKE, The Special Functions and Their Approximations. Vol. 1, Math. in Sci. and Engineering, vol. 53, Academic Press, New York and London, 1969. MR 39 #3039.
- J. D. Niblett, Some hypergeometric identities, Pacific J. Math. 2 (1952), 219–225. MR 47837
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725
- H. M. Srivastava, Generating functions for Jacobi and Laguerre polynomials, Proc. Amer. Math. Soc. 23 (1969), 590–595. MR 249694, DOI 10.1090/S0002-9939-1969-0249694-7 A. VERMA, "A class of expansions of G-functions and the Laplace transform," Math. Comp., v. 19, 1965, pp. 664-666.
- Arun Verma, Some transformations of series with arbitrary terms, Ist. Lombardo Accad. Sci. Lett. Rend. A 106 (1972), 342–353. MR 328144
- Arun Verma, On generating functions of classical polynomials, Proc. Amer. Math. Soc. 46 (1974), 73–76. MR 344537, DOI 10.1090/S0002-9939-1974-0344537-7 J. WIMP, "Polynomial approximation to integral transforms," Math. Comp., v. 15, 1961, pp. 174-178.
- Jet Wimp, Polynomial expansions of Bessel functions and some associated functions, Math. Comp. 16 (1962), 446–458. MR 148956, DOI 10.1090/S0025-5718-1962-0148956-3
- David Zeitlin, A new class of generating functions for hypergeometric polynomials, Proc. Amer. Math. Soc. 25 (1970), 405–412. MR 264123, DOI 10.1090/S0002-9939-1970-0264123-3
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 894-902
- MSC: Primary 41A10; Secondary 33A65
- DOI: https://doi.org/10.1090/S0025-5718-1975-0372472-6
- MathSciNet review: 0372472