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International Journal of Combinatorics
Volume 2011 (2011), Article ID 208260, 14 pages
Harmonic Numbers and Cubed Binomial Coefficients
Victoria University College, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia
Received 18 January 2011; Accepted 3 April 2011
Academic Editor: Toufik Mansour
Copyright © 2011 Anthony Sofo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- H. Chen, “Evaluations of some Variant Euler Sums,” Journal of Integer Sequences, vol. 9, no. 2, article 06.2.3, p. 9, 2006.
- K. N. Boyadzhiev, “Harmonic number identities via Euler's transform,” Journal of Integer Sequences, vol. 12, no. 6, article 09.6.1, p. 8, 2009.
- L. Euler, Opera Omnia, Series 1, vol. 15, Teubner, Berlin, Germany, 1917.
- P. Flajolet and B. Salvy, “Euler sums and contour integral representations,” Experimental Mathematics, vol. 7, no. 1, pp. 15–35, 1998.
- A. Basu, “A new method in the study of Euler sums,” Ramanujan Journal, vol. 16, no. 1, pp. 7–24, 2008.
- J. Sondow and E. W. Weisstein, Harmonic number. From MathWorld-A Wolfram Web Rescources, http://mathworld.wolfram.com/HarmonicNumber.html.
- H. Alzer, D. Karayannakis, and H. M. Srivastava, “Series representations for some mathematical constants,” Journal of Mathematical Analysis and Applications, vol. 320, no. 1, pp. 145–162, 2006.
- T. Mansour, “Combinatorial identities and inverse binomial coefficients,” Advances in Applied Mathematics, vol. 28, no. 2, pp. 196–202, 2002.
- A. Sofo, “Integral forms of sums associated with harmonic numbers,” Applied Mathematics and Computation, vol. 207, no. 2, pp. 365–372, 2009.
- A. Sofo, Computational techniques for the summation of series, Kluwer Academic Publishers/Plenum Publishers, New York, NY, USA, 2003.
- A. Sofo, “Sums of derivatives of binomial coefficients,” Advances in Applied Mathematics, vol. 42, no. 1, pp. 123–134, 2009.
- A. Sofo, “Harmonic numbers and double binomial coefficients,” Integral Transforms and Special Functions, vol. 20, no. 11-12, pp. 847–857, 2009.
- A. Sofo, “Harmonic sums and integral representations,” Journal of Applied Analysis, vol. 16, no. 2, pp. 265–277, 2010.
- K. S. Kölbig, “The polygamma function and the derivatives of the cotangent function for rational arguments,” CERN-IT-Reports CERN-CN 96-005, 1996.
- K. S. Kölbig, “The polygamma function for and ,” Journal of Computational and Applied Mathematics, vol. 75, no. 1, pp. 43–46, 1996.
- J. Choi and D. Cvijović, “Values of the polygamma functions at rational arguments,” Journal of Physics. A, vol. 40, no. 50, pp. 15019–15028, 2007.
- Wolfram Research Inc., Mathematica, Wolfram Research Inc., Champaign, Ill, USA.
- Y. A. Brychkov, Handbook of Special Functions, CRC Press, Boca Raton, Fla, USA, 2008.