An approximation connected with the exponential function
Authors:
K. Soni and R. P. Soni
Journal:
Proc. Amer. Math. Soc. 114 (1992), 909918
MSC:
Primary 41A60; Secondary 33B15
MathSciNet review:
1094506
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Abstract: Some recent techniques in the uniform asymptotic expansions of integrals are used to obtain an expansion for a function related to the exponential function. This function is associated with Ramanujan, Watson, Copson, and Buckholtz. The results obtained complement those given by Buckholtz.
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 M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards, Washington, DC, 1964. MR 0167642 (29:4914)
 [2]
 N. Bleistein, Uniform asymptotic expansion of integrals with stationary point near algebraic singularity, Comm. Pure Appl. Math. 19 (1966), 353370. MR 0204943 (34:4778)
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 J. D. Buckholtz, Concerning an approximation of Copson, Proc. Amer. Math. Soc. 14 (1963), 564568. MR 0151770 (27:1754)
 [4]
 E. T. Copson, An approximation connected with , Proc. Edinburgh Math. Soc. 3 (19321933), 201206.
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 D. S. Jones, Asymptotic behavior of integrals, SIAM Rev. 14 (1972), 268317. MR 0372499 (51:8706)
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 F. W. J. Olver, Asymptotics and special functions, Academic Press, New York, 1974. MR 0435697 (55:8655)
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 K. Soni and B. D. Sleeman, On uniform asymptotic expansions and associated polynomials, J. Math. Anal. Appl. 124 (1987), 561583. MR 887010 (88e:41066)
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 K. Soni and N. M. Temme, On a biorthogonal system associated with uniform asymptotic expansions, Centre for Mathematics and Computer Science, Amsterdam, Report AmR8709.
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 N. M. Temme, Special functions as approximants in uniform asymptotic expansions of integrals; A survey, Rend. Sem. Mat. Univ. Politecn. Torino, Special Issue, (1985), 289317. MR 850038 (87i:41026)
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 G. N. Watson, Approximation connected with , Proc. London Math. Soc. (2) 29 (192829), 293308.
 [11]
 R. Wong, On uniform asymptotic expansion of definite integrals, J. Approx. Theory 7 (1973), 7686. MR 0340910 (49:5660)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199210945068
PII:
S 00029939(1992)10945068
Article copyright:
© Copyright 1992
American Mathematical Society
