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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

The asymptotic expansion of the Meijer $ G$-function


Author: Jerry L. Fields
Journal: Math. Comp. 26 (1972), 757-765
MSC: Primary 33A35; Secondary 65D20
MathSciNet review: 0361202
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Abstract | References | Similar Articles | Additional Information

Abstract: Gamma function identities are integrated to expand the Meijer $ G$-function in a basic set of functions, each of which is simply characterized asymptotically.


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

  • [1] C. S. Meijer, ``On the $ G$-function. I-VIII,'' Nederl. Akad. Wetensch. Proc. Ser. A, v. 49, 1946, pp. 227-237, 344-356, 457-469, 632-641, 765-772, 936-943, 1063-1072, 1165-1175 = Indag. Math., v. 8, 1946, pp. 124-134, 213-225, 312-324, 391-400, 468-475, 595-602, 661-670, 713-723. MR 8, 156; MR 8, 379.
  • [2] Y. L. Luke, The Special Functions and Their Approximations. Vols. I, II, Math. in Sci. and Engineering, Vol. 53, Academic Press, New York, 1969. MR 39 #3039; MR 40 #2909.
  • [3] E. W. Barnes, ``The asymptotic expansion of integral functions defined by generalized hypergeometric series,'' Proc. London Math. Soc. (2), v. 5, 1907, pp. 59-116.
  • [4] Jerry L. Fields, A linear scheme for rational approximations, J. Approximation Theory 6 (1972), 161–175. Collection of articles dedicated to J. L. Walsh on his 75th birthday, VI (Proc. Internat. Conf. Approximation Theory, Related Topics and their Applications, Univ. Maryland, College Park, Md., 1970). MR 0346383 (49 #11108)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0361202-7
PII: S 0025-5718(1972)0361202-7
Keywords: Meijer $ G$-functions, asymptotic expansions, linear differential equations, irregular singular points
Article copyright: © Copyright 1972 American Mathematical Society