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Series expansions of $ W\sb{k,\,m}(Z)$ involving parabolic cylinder functions

Authors: R. Wong and E. Rosenbloom
Journal: Math. Comp. 25 (1971), 783-787
MSC: Primary 33A30
MathSciNet review: 0306566
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Abstract: In this paper, an explicit error bound is obtained for an expansion of the Whittaker function, $ {W_{k,m}}(z)$, in series of parabolic cylinder functions. It is also shown that the Whittaker function may be asymptotically represented as the sum of two products where one product involves a parabolic cylinder function and the other product involves the first-order derivative of this function.

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  • [1] H. Buchholz, Die konfluente hypergeometrische Funktion mit besonderer Berücksichtigung ihrer Anwendungen, Ergebnisse der Angew. Mathematik, Band 2, Springer-Verlag, Berlin, 1953; English transl., Springer Tracts in Natural Philosophy, vol. 15, Springer-Verlag, New York, 1969. MR 14, 978; MR 39 #1692. MR 0054783 (14:978e)
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Keywords: Whittaker function, parabolic cylinder functions, error bound, asymptotic representation
Article copyright: © Copyright 1971 American Mathematical Society

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