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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
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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 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

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Keywords: Complete elliptic integrals, generalized hypergeometric series
Article copyright: © Copyright 1971 American Mathematical Society

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