226
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Fourier series for elliptic integrals and some generalizations via hypergeometric series

Pages 305-315 | Received 11 Sep 2007, Published online: 28 Oct 2008

References

  • Abramowitz , M. and Stegun , I. S. 1972 . Handbook of Mathematical Functions , New York : Dover .
  • Byrd , P. F. and Friedman , M. D. 1971 . Handbook of Elliptic Integrals for Engineers and Scientists , 2 , Berlin : Springer .
  • Conway , J. T. 2006 . Fourier series for the Legendre elliptic integrals . Integral Transforms Spec. Funct. , 17 ( 7 ) : 499 – 505 .
  • Conway , J. T. 2007 . Fourier and other series containing associated Legendre functions for incomplete Epstein-Hubbell integrals and functions related to elliptic integrals . Integral Transforms Spec. Funct. , 18 ( 3 ) : 179 – 191 .
  • Epstein , L. F. and Hubbell , J. H. 1963 . Evaluation of a generalized elliptic-type integral . J. Res. Nat. Bur. Stand. , 67 ( B ) : 1 – 17 .
  • Erdélyi , A. 1953 . Higher Transcendental Functions Vol. 2 , New York : McGraw-Hill .
  • Gradshteyn , I. S. and Ryzhik , I. M. 2007 . Table of Integrals, Series and Products , 7 , New York : Academic .
  • Gröbner , W. and Hofreiter , N. 1957 . Integraltafel, Vol. 1 , 2 , Vienna : Springer .
  • Prudnikov , A. P. , Brychkov , Yu. A. and Marichev , O. I. 1986 . Integrals and Series Vol. 1: Elementary Functions , New York : Gordon and Breach .
  • Prudnikov , A. P. , Brychkov , Yu. A. and Marichev , O. I. 1990 . Integrals and Series Vol. 3: More Special Functions , New York : Gordon and Breach .
  • Selfridge , R. G. and Maxfield , J. E. 1958 . Table of the Incomplete Elliptic Integral of the Third Kind , New York : Dover .
  • Slater , L. J. 1966 . Generalized Hypergeometric Functions , Cambridge : Cambridge University Press .
  • Srivastava , H. M. and Karlsson , P. W. 1985 . Multiple Gaussian Hypergeometric Series , Chichester : Ellis Horwood .
  • Whittaker , E. T. and Watson , G. N. 1927 . A Course of Modern Analysis , 4 , Cambridge : Cambridge University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.