Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

A closed form evaluation of the elliptic integral


Authors: M. L. Glasser and V. E. Wood
Journal: Math. Comp. 25 (1971), 535-536
DOI: https://doi.org/10.1090/S0025-5718-71-99714-6
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: The complete elliptic integral of the first kind $ K(k)$ is evaluated in terms of gamma functions for the moduli $ k = \surd 2 - 1$ and $ {(2\surd 2 - 2)^{1/2}}$.


References [Enhancements On Off] (What's this?)

  • [1] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469
  • [2] M. L. Glasser, ``An elliptic integral identity,'' Math. Comp., v. 25, 1971, pp. 533-534.
  • [3] W. N. Bailey, Generalized Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1935.
  • [4] Bruce C. Berndt, Introduction to Ramanujan’s modular equations, Proceedings of the Ramanujan Centennial International Conference (Annamalainagar, 1987) RMS Publ., vol. 1, Ramanujan Math. Soc., Annamalainagar, 1988, pp. 15–20. MR 993339


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-71-99714-6
Keywords: Complete elliptic integrals, generalized hypergeometric series
Article copyright: © Copyright 1971 American Mathematical Society