Recurrence relations for hypergeometric functions of unit argument
Author:
Stanisław Lewanowicz
Journal:
Math. Comp. 45 (1985), 521535
MSC:
Primary 33A35; Secondary 65Q05
Corrigendum:
Math. Comp. 48 (1987), 853.
Corrigendum:
Math. Comp. 48 (1987), 853854.
MathSciNet review:
804941
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We show that the generalized hypergeometric function satisfies a nonhomogeneous recurrence relation of order , where when is balanced, and otherwise. Also, for a homogeneous recurrence relation of order is given.
 [1]
A. Erdélyi et al., Higher Transcendental Functions, Vol. 1, McGrawHill, New York, 1953.
 [2]
Shyam
L. Kalla, Salvador
Conde, and Yudell
L. Luke, Integrals of Jacobi
functions, Math. Comp. 38
(1982), no. 157, 207–214. MR 637298
(83a:33005), http://dx.doi.org/10.1090/S00255718198206372988
 [3]
Samuel
Karlin and James
L. McGregor, The Hahn polynomials, formulas and an
application, Scripta Math. 26 (1961), 33–46. MR 0138806
(25 #2249)
 [4]
Y. L. Luke, The Special Functions and Their Approximations, 2 vols., Academic Press, New York, 1969.
 [5]
Lucy
Joan Slater, Generalized hypergeometric functions, Cambridge
University Press, Cambridge, 1966. MR 0201688
(34 #1570)
 [6]
J.
A. Wilson, Threeterm contiguous relations and some new orthogonal
polynomials, Padé and rational approximation (Proc. Internat.
Sympos., Univ. South Florida, Tampa, Fla., 1976) Academic Press, New
York, 1977, pp. 227–232. MR 0466671
(57 #6548)
 [7]
James
A. Wilson, Some hypergeometric orthogonal polynomials, SIAM J.
Math. Anal. 11 (1980), no. 4, 690–701. MR 579561
(82a:33014), http://dx.doi.org/10.1137/0511064
 [8]
Jet
Wimp, Recursion formulae for hypergeometric
functions, Math. Comp. 22 (1968), 363–373. MR 0226065
(37 #1655), http://dx.doi.org/10.1090/S00255718196802260658
 [9]
Jet
Wimp, The computation of ₃𝐹₂(1),
Internat. J. Comput. Math. 10 (1981/82), no. 1,
55–62. MR
644716 (83d:65053), http://dx.doi.org/10.1080/00207168108803266
 [10]
Jet
Wimp, Differentialdifference properties of
hypergeometric polynomials, Math. Comp. 29 (1975), 577–581.
MR
0440085 (55 #12966), http://dx.doi.org/10.1090/S00255718197504400853
 [11]
J. Wimp, "Irreducible recurrence relations and representation theorems for ," Comput. Math. Appl., v. 9, 1983, pp. 669678.
 [12]
S.
Lewanowicz, On the differentialdifference
properties of the extended Jacobi polynomials, Math. Comp. 44 (1985), no. 170, 435–441. MR 777275
(86c:33001), http://dx.doi.org/10.1090/S00255718198507772752
 [1]
 A. Erdélyi et al., Higher Transcendental Functions, Vol. 1, McGrawHill, New York, 1953.
 [2]
 S. L. Kalla, S. Conde & Y. L. Luke, "Integrals of Jacobi functions," Math. Comp., v. 38, 1982, pp. 207214. MR 637298 (83a:33005)
 [3]
 S. Karlin & J. L. McGregor, "The Hahn polynomials, formulas and an application," Scripta Math., v. 26, 1961, pp. 3346. MR 0138806 (25:2249)
 [4]
 Y. L. Luke, The Special Functions and Their Approximations, 2 vols., Academic Press, New York, 1969.
 [5]
 L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. MR 0201688 (34:1570)
 [6]
 J. A. Wilson, "Threeterm contiguous relations and some new orthogonal polynomials," in Padé and Rational Approximation (E. B. Saff and R. S. Varga, eds.), Academic Press, New York, 1977, pp. 227232. MR 0466671 (57:6548)
 [7]
 J. A. Wilson, "Some hypergeometric orthogonal polynomials," SIAM J. Math. Anal., v. 11, 1980, pp. 691701. MR 579561 (82a:33014)
 [8]
 J. Wimp, "Recursion formulae for hypergeometric functions," Math. Comp., v. 22, 1968, pp. 363373. MR 0226065 (37:1655)
 [9]
 J. Wimp, "The computation of ," Internat. J. Comput. Math., v. 10, 1981, pp. 5562. MR 644716 (83d:65053)
 [10]
 J. Wimp, "Differentialdifference properties of hypergeometric polynomials," Math. Comp., v. 29, 1975, pp. 577581. MR 0440085 (55:12966)
 [11]
 J. Wimp, "Irreducible recurrence relations and representation theorems for ," Comput. Math. Appl., v. 9, 1983, pp. 669678.
 [12]
 S. Lewanowicz, "On the differentialdifference properties of the extended Jacobi polynomials," Math. Comp., v. 44, 1985, pp. 435441. MR 777275 (86c:33001)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
33A35,
65Q05
Retrieve articles in all journals
with MSC:
33A35,
65Q05
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198508049412
PII:
S 00255718(1985)08049412
Article copyright:
© Copyright 1985
American Mathematical Society
