Polynomial expansions

Authors:
Jerry L. Fields and Mourad E. H. Ismail

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given.

**[1]**Ralph P. Boas Jr. and R. Creighton Buck,*Polynomial expansions of analytic functions*, Second printing, corrected. Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Bd. 19, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin, 1964. MR**0162914****[2]**J. W. Brown,*On zero type sets of Laguerre polynomials*, Duke Math. J.**35**(1968), 821–823. MR**0234027****[3]**J. W. Brown,*New generating functions for classical polynomials*, Proc. Amer. Math. Soc.**21**(1969), 263–268. MR**0236438**, https://doi.org/10.1090/S0002-9939-1969-0236438-8**[4]**L. Carlitz,*Some generating functions for Laguerre polynomials*, Duke Math. J.**35**(1968), 825–827. MR**0240351****[5]**Jerry L. Fields and Jet Wimp,*Expansions of hypergeometric functions in hypergeometric functions.*, Math. Comp.**15**(1961), 390–395. MR**0125992**, https://doi.org/10.1090/S0025-5718-1961-0125992-3**[6]**Jerry L. Fields and Jet Wimp,*Basic series corresponding to a class of hypergeometric polynomials*, Proc. Cambridge Philos. Soc.**59**(1963), 599–605. MR**0150350****[7]**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**0338484**, https://doi.org/10.1137/0505022**[8]**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.**[9]**J. D. Niblett,*Some hypergeometric identities*, Pacific J. Math.**2**(1952), 219–225. MR**0047837****[10]**Earl D. Rainville,*Special functions*, The Macmillan Co., New York, 1960. MR**0107725****[11]**H. M. Srivastava,*Generating functions for Jacobi and Laguerre polynomials*, Proc. Amer. Math. Soc.**23**(1969), 590–595. MR**0249694**, https://doi.org/10.1090/S0002-9939-1969-0249694-7**[12]**A. VERMA, "A class of expansions of*G*-functions and the Laplace transform,"*Math. Comp.*, v. 19, 1965, pp. 664-666.**[13]**Arun Verma,*Some transformations of series with arbitrary terms*, Ist. Lombardo Accad. Sci. Lett. Rend. A**106**(1972), 342–353. MR**0328144****[14]**Arun Verma,*On generating functions of classical polynomials*, Proc. Amer. Math. Soc.**46**(1974), 73–76. MR**0344537**, https://doi.org/10.1090/S0002-9939-1974-0344537-7**[15]**J. WIMP, "Polynomial approximation to integral transforms,"*Math. Comp.*, v. 15, 1961, pp. 174-178.**[16]**Jet Wimp,*Polynomial expansions of Bessel functions and some associated functions*, Math. Comp.**16**(1962), 446–458. MR**0148956**, https://doi.org/10.1090/S0025-5718-1962-0148956-3**[17]**David Zeitlin,*A new class of generating functions for hypergeometric polynomials.*, Proc. Amer. Math. Soc.**25**(1970), 405–412. MR**0264123**, https://doi.org/10.1090/S0002-9939-1970-0264123-3

Retrieve articles in *Mathematics of Computation*
with MSC:
41A10,
33A65

Retrieve articles in all journals with MSC: 41A10, 33A65

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0372472-6

Keywords:
Polynomial expansions,
hypergeometric functions

Article copyright:
© Copyright 1975
American Mathematical Society