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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
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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 & G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, New York, 1962, sect. 22.81. MR 31 #2375. MR 1424469 (97k:01072)
  • [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] S. Ramanujan, ``Modular equations and approximations to $ \pi $,'' Quart. J. Math., v. 45, 1914, pp. 350-372, sect. 15. MR 993339 (90d:11055)


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

American Mathematical Society