Expansions of hypergeometric functions in hypergeometric functions
Authors:
Jerry L. Fields and Jet Wimp
Journal:
Math. Comp. 15 (1961), 390395
MSC:
Primary 33.20
MathSciNet review:
0125992
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Abstract: In [1] Luke gave an expansion of the confluent hypergeometric function in terms of the modified Bessel functions . The existence of other, similar expansions implied that more general expansions might exist. Such was the case. Here multiplication type expansions of loworder hypergeometric functions in terms of other hypergeometric functions are generalized by Laplace transform techniques.
 [1]
Yudell
L. Luke, Expansion of the confluent
hypergeometric function in series of Bessel functions, Math. Tables Aids Comput. 13 (1959), 261–271. MR 0107027
(21 #5754), http://dx.doi.org/10.1090/S00255718195901070272
 [2]
A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, McGrawHill Book Company, Inc., 1953, Vol. 1. Hereafter in this list, we use the abbreviation H.T.F.
 [3]
Yudell
L. Luke and Richard
L. Coleman, Expansion of hypergeometric functions
in series of other hypergeometric functions, Math. Comp. 15 (1961), 233–237. MR 0123745
(23 #A1067), http://dx.doi.org/10.1090/S00255718196101237453
 [4]
A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, Vol. 1, McGrawHill Book Company, Inc., 1954.
 [5]
E.
D. Rainville, Certain generating functions and associated
polynomials, Amer. Math. Monthly 52 (1945),
239–250. MR 0011751
(6,211e)
 [6]
T.
W. Chaundy, An extension of hypergeometric functions. I,
Quart. J. Math., Oxford Ser. 14 (1943), 55–78. MR 0010749
(6,64d)
 [7]
C. S. Meijer, ``Expansion theorems for the Gfunction,'' Indag. Math., v. 1417, 195255.
 [8]
H.T.F., Vol. 2.
 [9]
J. L. Fields & Y. L. Luke, ``Asymptotic expansions of a class of hypergeometric polynomials with respect to the order,'' Midwest Research Institute Technical Report, July 1, 1959.
 [10]
G.
N. Watson, A treatise on the theory of Bessel functions,
Cambridge Mathematical Library, Cambridge University Press, Cambridge,
1995. Reprint of the second (1944) edition. MR 1349110
(96i:33010)
 [1]
 Y. L. Luke, ``Expansion of the confluent hypergeometric function in series of Bessel functions,'' MTAC, v. 13, 1959, p. 261271. MR 0107027 (21:5754)
 [2]
 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, McGrawHill Book Company, Inc., 1953, Vol. 1. Hereafter in this list, we use the abbreviation H.T.F.
 [3]
 Y. L. Luke & Richard L. Coleman, ``Expansion of hypergeometric functions in series of other hypergeometric functions,'' Math. Comp., v. 15, 1961, p. 233. MR 0123745 (23:A1067)
 [4]
 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, Vol. 1, McGrawHill Book Company, Inc., 1954.
 [5]
 E. D. Rainville, ``Certain generating functions and their associated polynomials,'' Amer. Math. Monthly, v. 52, No. 5, May 1945, or H.T.F., Vol. 3, p. 239250. MR 0011751 (6:211e)
 [6]
 T. W. Chaundy, ``An extension of hypergeometric functions,'' Quart. J. Math. Oxford Ser. 14, 1943, p. 5578. MR 0010749 (6:64d)
 [7]
 C. S. Meijer, ``Expansion theorems for the Gfunction,'' Indag. Math., v. 1417, 195255.
 [8]
 H.T.F., Vol. 2.
 [9]
 J. L. Fields & Y. L. Luke, ``Asymptotic expansions of a class of hypergeometric polynomials with respect to the order,'' Midwest Research Institute Technical Report, July 1, 1959.
 [10]
 G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1945. MR 1349110 (96i:33010)
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DOI:
http://dx.doi.org/10.1090/S00255718196101259923
PII:
S 00255718(1961)01259923
Article copyright:
© Copyright 1961
American Mathematical Society
