An asymptotic expansion of $W_{k, m}(z)$ with large variable and parameters
HTML articles powered by AMS MathViewer
- by R. Wong PDF
- Math. Comp. 27 (1973), 429-436 Request permission
Abstract:
In this paper, we obtain an asymptotic expansion of the Whittaker function ${W_{k,m}}(z)$ when the parameters and variable are all large but subject to the growth restrictions that $k = o(z)$ and $m = o({z^{1/2}})$ as $z \to \infty$. Here, it is assumed that k and m are real and $|\arg z|\; \leqq \;\pi - \delta$.References
-
H. Buchholz, The Confluent Hypergeometric Function, Springer-Verlag, Berlin, 1969.
- Chieh-Chien Chang, Boa-Teh Chu, and Vivian O’Brien, An asymptotic expansion of the Whittaker function $w_{k,m}(z)$, J. Rational Mech. Anal. 2 (1953), 125–135. MR 51374, DOI 10.1512/iumj.1953.2.52007
- E. T. Copson, Asymptotic expansions, Cambridge Tracts in Mathematics, vol. 55, Cambridge University Press, Cambridge, 2004. Reprint of the 1965 original. MR 2139829 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions. Vol. 2, McGraw-Hill, New York, 1953. MR 15, 419.
- A. Erdélyi and C. A. Swanson, Asymptotic forms of Whittaker’s confluent hypergeometric functions, Mem. Amer. Math. Soc. 25 (1957), 49. MR 90678
- A. Erdélyi and M. Wyman, The asymptotic evaluation of certain integrals, Arch. Rational Mech. Anal. 14 (1963), 217–260. MR 157170, DOI 10.1007/BF00250704
- Nicholas D. Kazarinoff, Asymptotic forms for the Whittaker functions with both parameters large, J. Math. Mech. 6 (1957), 341–360. MR 0086152, DOI 10.1512/iumj.1957.6.56016
- L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, New York, 1960. MR 0107026
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
- R. Wong, On uniform asymptotic expansion of definite integrals, J. Approximation Theory 7 (1973), 76–86. MR 340910, DOI 10.1016/0021-9045(73)90055-5
- R. Wong and E. Rosenbloom, Series expansions of $W_{k,\,m}(Z)$ involving parabolic cylinder functions, Math. Comp. 25 (1971), 783–787. MR 306566, DOI 10.1090/S0025-5718-1971-0306566-4
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 429-436
- MSC: Primary 33A30
- DOI: https://doi.org/10.1090/S0025-5718-1973-0328145-7
- MathSciNet review: 0328145