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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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 | References | Similar Articles | Additional Information

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.


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

  • [1] Herbert Buchholz, Die konfluente hypergeometrische Funktion mit besonderer Berücksichtigung ihrer Anwendungen, Ergebnisse der angewandten Mathematik. Bd. 2, Springer-Verlag, Berlin, 1953 (German). MR 0054783 (14,978e)
  • [2] A. Erdélyi, W. Magnus, F. Oberhettinger & F. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. MR 15. 419.
  • [3] Artur Erdélyi, Über eine Integraldarstellung der 𝑊^{𝑘,𝑚}-Funktionen und ihre Darstellung durch die Funktionen des parabolischen Zylinders, Math. Ann. 113 (1937), no. 1, 347–356 (German). MR 1513095, http://dx.doi.org/10.1007/BF01571638
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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0306566-4
PII: S 0025-5718(1971)0306566-4
Keywords: Whittaker function, parabolic cylinder functions, error bound, asymptotic representation
Article copyright: © Copyright 1971 American Mathematical Society