Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T13:13:45.208Z Has data issue: false hasContentIssue false
  • English
  • Français

The expansion of Lamé functions into series of associated Legendre functions of the second kind

Published online by Cambridge University Press:  24 October 2008

B. D. Sleeman
B. D. Sleeman
Affiliation:
Department of Mathematics, Battersea College of Technology, London, S.W. 11
Get access Rights & Permissions [Opens in a new window]

Extract

Introduction. In this paper, a study is made of the solutions of Lamé's differential equation as series of associated Legendre functions. The particular feature studied is the representation of the second solution corresponding to the case when the first solution is a Lamé polynomial.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 441 - 452
Copyright
Copyright © Cambridge Philosophical Society 1966

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)Erdélyi, A.Expansions of Lamé Functions into series of Legendre functions. Proc. Boy. Soc. Edinburgh 27 (1948), 247–267.Google Scholar
(2)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge University Press, 1927).Google Scholar
(3)Lambe, C. G. and Ward, D. R.Some differential equations and associated integral equations. Quart. J. Math. Oxford Ser. 2, 5 (1934), 81–97.CrossRefGoogle Scholar
(4)Ince, E. L.Periodic Lame functions. Proc. Roy. Soc. Edinburgh 60 (1940), 47–63.Google Scholar
(5)Arscott, F. M.Integral equations and relations for Lame functions. Quart. J. Math. Oxford Ser. 2, 15 (1964), 103–115.CrossRefGoogle Scholar
(6)Arscott, F. M.Periodic differential equations (Pergamon Press, 1964).Google Scholar
(7)Erdélyi, A.Higher transcendental functions, Vol. i (McGraw-Hill, 1953).Google Scholar
(8)Schäfke, F. W.Einführung in der Theorie der speziellen Functionen der Mathematischen Physih (Springer, 1963).Google Scholar
(9)Hobson, E. W.The theory of spherical and ellipsoidal harmonics (1931).Google Scholar
(10)Perron, O.Die Lehre von den Kettenbrüchen, Vol. ii (Teubner; Stuttgart, 1957).Google Scholar