Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-10T20:34:59.896Z Has data issue: false hasContentIssue false
  • English
  • Français

Expansions of the Poiseuille and the irregular Coulomb functions

Published online by Cambridge University Press:  24 October 2008

A. S. Meligy
A. S. Meligy
Affiliation:
Institute for Theoretical PhysicsUniversity of Copenhagen, Denmark
Get access Rights & Permissions [Opens in a new window]

Abstract

An expansion of the Whittaker function Mk, m(z) in terms of functions of the same kind is obtained. It generalizes previous results and is used to derive expansions of the second Whittaker function Wk,m (z) in terms of the M functions for the cases m = 0 and ½. The case m = 0 provides expansions for the Poiseuille and the exponential integral functions. The case m = ½ provides an expansion for the irregular Coulomb wave function having angular momentum zero in terms of the regular Coulomb functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 782 - 789
Copyright
Copyright © Cambridge Philosophical Society 1961

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)Abramowitz, M., Tables of Coulomb wave functions. National Bureau of Standards, App. Math, series 17 (Washington, 1952).Google Scholar
(2)Bailey, W. N., Generalized hypergeometric series (Cambridge, 1935).Google Scholar
(3)Buchholz, H., Die Konfluente Hypergeometrische Funktion (Berlin, 1953).CrossRefGoogle Scholar
(4)Fröberg, C., Rev. Mod. Phys. 27 (1955), 399.CrossRefGoogle Scholar
(5)Lauwerier, H. A., Appl. Sci. Res. A, 3 (1951), 58.CrossRefGoogle Scholar
(6)Meligy, A. S., Nuclear Phys. 1 (1956), 610.CrossRefGoogle Scholar
(7)Meligy, A. S., Nuclear Phys. 5 (1958), 615.CrossRefGoogle Scholar
(8)Meligy, A. S., Proc. Phys. Soc. 71 (1958), 1017.CrossRefGoogle Scholar
(9)Meligy, A. S., Quart. J. Math. (2), 10 (1959), 202.CrossRefGoogle Scholar
(10)Meligy, A. S., Proc. Camb. Phil. Soc. 56 (1960), 233.CrossRefGoogle Scholar
(11)Slater, L. J., Proc. Camb. Phil. Soc. 50 (1954), 628.CrossRefGoogle Scholar
(12)Slater, L. J., Confluent hypergeometric functions (Cambridge, 1960).Google Scholar
(13)Whittaker, E. T. and Watson, G. N., Modern anaylsis, 4th ed. (Cambridge, 1927).Google Scholar