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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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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:
https://doi.org/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:
November 2013
Authors:
Edigles Guedes, Raja Rama Gandhi
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Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

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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