The asymptotic expansion of the Meijer -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 -function in a basic set of functions, each of which is simply characterized asymptotically.

**[1]**C. S. Meijer, ``On the -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**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1972-0361202-7

Keywords:
Meijer -functions,
asymptotic expansions,
linear differential equations,
irregular singular points

Article copyright:
© Copyright 1972
American Mathematical Society