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The asymptotic expansion of a hypergeometric function $ \sb{2}F\sb{2}(1,\,\alpha ;\,\rho \sb{1},\,\rho \sb{2};\,\ z)$


Author: Shoon K. Kim
Journal: Math. Comp. 26 (1972), 963
MSC: Primary 65D20; Secondary 33A30
DOI: https://doi.org/10.1090/S0025-5718-1972-0314235-0
MathSciNet review: 0314235
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Abstract: The asymptotic expansion of a hypergeometric function $ _2{F_2}(1,\alpha ;{\rho _1},{\rho _2};z)$ is given in terms of hypergeometric functions $ _2{F_0}({z^{ - 1}})$ and $ _3{F_1}({z^{ - 1}})$.


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

  • [1] Shoon K. Kim, J. Chem. Phys., v.46, 1967, p. 123.
  • [2] Yudell L. Luke Integrals of Bessel Functions, McGraw-Hill, New York, 1962, p. 14, Eq. (38). MR 25 #5198. MR 0141801 (25:5198)
  • [3] Yudell L. Luke, The Special Functions and Their Approximations. Vol. I, Math. in Sci. and Engineering, vol. 53, Academic Press, New York, 1969. MR 39 #3039. MR 0241700 (39:3039)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0314235-0
Keywords: Hypergeometric functions, asymptotic expansion
Article copyright: © Copyright 1972 American Mathematical Society

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