A closed form evaluation of the elliptic integral
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- by M. L. Glasser and V. E. Wood PDF
- Math. Comp. 25 (1971), 535-536 Request permission
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
- 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, DOI 10.1017/CBO9780511608759 M. L. Glasser, “An elliptic integral identity,” Math. Comp., v. 25, 1971, pp. 533-534. W. N. Bailey, Generalized Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1935.
- 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
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 535-536
- DOI: https://doi.org/10.1090/S0025-5718-71-99714-6