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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.28 no.1 Antofagasta May 2009

http://dx.doi.org/10.4067/S0716-09172009000100004 

Proyecciones Journal of Mathematics
Vol. 28, No 1, pp. 35—45, May 2009.
Universidad Católica del Norte
Antofagasta - Chile


ON SUMS OF BINOMIAL COEFFICIENTS


ANTHONY SOFO

Victoria University, Australia.


Correspondencia a:


Abstract
We investigate the integral representation of infinite sums involving the ratio of binomial coefficients. We also recover some wellknown properties of ζ (3) and extend the range of results given by other authors.


Subjclass [2000] : Primary 11B65. Secondary 05A10, 05A19, 33C20, 33D60.
Keywords : Triple binomial coefficients, combinatorial identities, integral representations, Zeta function.

REFERENCES
[1] R. Apéry. Irrationalitè ζ (2) and ζ (3) , Journees Arithmètiques de Luminy, Ast érisque, 61, pp. 11-13,         [ Links ](1979).
[2] F. Beukers. A note on the irrationality of ζ (2) and ζ (3) . Bull. London Math. Soc., 11 , pp. 268-272,         [ Links ](1979).
[3] G.Rhin and C.Viola. The group structure for ζ (3) , Acta Arith. 97. 3, pp. 269-293,         [ Links ](2001).
[4] A. Sofo. Integral forms of sums associated with harmonic numbers, Appl. Maths. Comput., 207, pp. 356-372,         [ Links ](2009).
[5] A. Sofo. General properties involving reciprocals of binomial coefficients. Journal of Integer Sequences, 9, article 06.4.5,         [ Links ](2006).
[6] A. Sofo. Computational Techniques for the Summation of Series. Kluwer Academic/Plenum Publishers,         [ Links ](2003).
[7] A. Sofo. Sums of derivatives of binomial coefficients. Adv Applied Maths, 42 (2009), pp. 123-134,         [ Links ](2009).
[8] A. Sofo. Convexity properties of Reciprocals of binomial coefficients. Numerical Analysis and Applied Mathematics, (2007) Editor T. E. Simos, AIP, Melville, New York, pp. 70         [ Links ]3-706.
[9] http://mathworld.wolfram.com/RiemannZetaFunction.html.
        [ Links ]

ANTHONY SOFO
School of Engineering and Science
Research Group in Mathematical Inequalities and Applications
Victoria University
P. O. Box 14428
Melbourne City
VIC 8001
Australia
e-mail : anthony.sofo@vu.edu.au

Received : May 2008. Accepted : March 2009

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