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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Series expansions of $W_{k, m}(Z)$ involving parabolic cylinder functions
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by R. Wong and E. Rosenbloom PDF
Math. Comp. 25 (1971), 783-787 Request permission

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
  • Herbert Buchholz, Die konfluente hypergeometrische Funktion mit besonderer Berücksichtigung ihrer Anwendungen, Ergebnisse der angewandten Mathematik. Bd. 2, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1953 (German). MR 0054783, DOI 10.1007/978-3-642-53371-6
  • A. Erdélyi, W. Magnus, F. Oberhettinger & F. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. MR 15. 419.
  • 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, DOI 10.1007/BF01571638
  • G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • 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
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 783-787
  • MSC: Primary 33A30
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0306566-4
  • MathSciNet review: 0306566