Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On the differential-difference properties of the extended Jacobi polynomials


Author: S. Lewanowicz
Journal: Math. Comp. 44 (1985), 435-441
MSC: Primary 33A30
DOI: https://doi.org/10.1090/S0025-5718-1985-0777275-2
MathSciNet review: 777275
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss differential-difference properties of the extended Jacobi polynomials

$\displaystyle {P_n}(x){ = _{p + 2}}{F_q}( - n,n + \lambda ,{a_p};{b_q};x)\quad (n = 0,1, \ldots ).$

The point of departure is a corrected and reformulated version of a differential-difference equation satisfied by the polynomials $ {P_n}(x)$, which was derived by Wimp (Math. Comp., v. 29, 1975, pp. 577-581).

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

  • [1] W. N. Bailey, "Contiguous hypergeometric functions of the type $ _3{F_2}(1)$," Proc. Glasgow Math. Assoc., v. 2, 1954, pp. 62-65. MR 0064918 (16:356e)
  • [2] S. Lewanowicz, Recurrence Relations for Hypergeometric Functions of Unit Argument, Report N-127, Inst. Computer Sci., Univ. of Wroclaw, 1983. Also Math. Comp., v. 45, 1985. (To appear.) MR 804941 (86m:33004)
  • [3] Y. L. Luke, The Special Functions and Their Approximations, Academic Press, New York, 1969.
  • [4] Y. L. Luke, Mathematical Functions and Their Approximations, Academic Press, New York, 1975. MR 0501762 (58:19039)
  • [5] Jet Wimp, "Recursion formulae for hypergeometric functions," Math. Comp., v. 22, 1968, pp. 363-373. MR 0226065 (37:1655)
  • [6] Jet Wimp, "Differential-difference properties of hypergeometric polynomials," Math. Comp., v. 29, 1975, pp. 577-581. MR 0440085 (55:12966)
  • [7] E. D. Rainville, Special Functions, Macmillan, New York, 1960. MR 0107725 (21:6447)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 33A30

Retrieve articles in all journals with MSC: 33A30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0777275-2
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society