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 is evaluated in terms of gamma functions for the moduli and .

**[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