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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
  • 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:
  • MathSciNet review: 0306566