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The asymptotic expansion of the Meijer $ G$-function


Author: Jerry L. Fields
Journal: Math. Comp. 26 (1972), 757-765
MSC: Primary 33A35; Secondary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1972-0361202-7
MathSciNet review: 0361202
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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] J. L. Fields, ``A linear scheme for rational approximations,'' J. Approximation Theory, v. 6, 1972. (To appear.) MR 0346383 (49:11108)

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Additional Information

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

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