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On the Complete Elliptic Integrals and Babylonian Identity I: The 1/Π Formulaes Involving Gamma Functions and Summations

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Abstract:

We evaluate the constant 1/Π using the Babylonian identity and complete elliptic integral of first kind. This resulted in two representations in terms of the Euler’s gamma functions and summations.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 6)
Pages:
40-46
DOI:
10.18052/www.scipress.com/BMSA.6.40
Citation:
E. Guedes and R. R. Gandhi, "On the Complete Elliptic Integrals and Babylonian Identity I: The 1/Π Formulaes Involving Gamma Functions and Summations", Bulletin of Mathematical Sciences and Applications, Vol. 6, pp. 40-46, 2013
Online since:
Nov 2013
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References:

Havil, Julian, Gamma: Exploring the Euler's Constant, Princeton University Press, (2003).

Slater, Lucy Joan, Generalized Hypergeometric Functions, Cambridge University Press, (1966).

http: /en. wikipedia. org/wiki/Elliptic_integral, available in July 02, (2012).

Armitage, J. V. and Eberlein, W. F., Elliptic Functions, Cambridge University Press, (2006).

Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, Academic Press, (2000).

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