Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T01:43:37.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Expansions of certain Whittaker functions

Published online by Cambridge University Press:  24 October 2008

A. S. Meligy
A. S. Meligy
Affiliation:
Faculty of ScienceUniversity of AlexandriaAlexandriaEgypt
Get access Rights & Permissions [Opens in a new window]

Abstract

An expansion of the Whittaker function Wk, m(z) in terms of Bessel functions is given for 2m an integer or zero. Simple formulae are derived for the cases of m = 0, ½, 1 and . The case m = 0 provides expansions for the exponential, sine, cosine and similar integrals. The cases m = ½ and provide expansions for the irregular Coulomb wave functions having angular momenta zero and one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 3 , July 1960 , pp. 233 - 239
Copyright
Copyright © Cambridge Philosophical Society 1960

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Abramowttz, M.Tables of Coulomb wave functions, National Bureau of Standards, Appl. Math, series 17. (Washington, 1952).Google Scholar
(2)Abramowitz, M.J. Math. Phys. 33 (1954), 111.CrossRefGoogle Scholar
(3)Breit, G. and Hull, M.Phys. Rev. 80 (1950), 561.CrossRefGoogle Scholar
(4)Fröberg, C.Rev. Mod. Phys. 27 (1955), 399.CrossRefGoogle Scholar
(5)Meligy, A. S.Nuclear Phys. 1 (1956), 610.CrossRefGoogle Scholar
(6)Meligy, A. S.Nuclear Phys. 5 (1958), 615.CrossRefGoogle Scholar
(7)Meligy, A. S.Quart. J. Math. 10 (1959), 202.CrossRefGoogle Scholar
(8)NATIONAL BUREAU OF STANDARDS. Tables of spherical Bessel functions, vols. I and II (New York, 1947).Google Scholar
(9)Powell, J. L.Phys. Rev. 72 (1947), 626.CrossRefGoogle Scholar
(10)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge, 1927).Google Scholar
(11)Buchholż, H.Die Konfluente Hypergeometrische Funktion (Berlin, 1953).CrossRefGoogle Scholar