Abstract
We develop new families of closed-form representations of sums of alternating harmonic numbers and reciprocal squared binomial coefficients including integral representations.
Similar content being viewed by others
References
Adamchik V., Srivastava H.M.: Some series of the zeta and related functions. Analysis 18(2), 131–144 (1998)
Borwein J.M., Zucker I.J., Boersma J.: The evaluation of character Euler double sums. Ramanujan J. 15, 377–405 (2008)
Choi, J., Cvijović, D.: Values of the polygamma functions at rational arguments. J. Phys. A Math. Theor. 40, 15019–15028 (2007). [Corrigendum, ibidem, 43, 239801 (2010) (1 p)]
Choi, J.: Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers. J. Inequal. Appl. 2013, 49 (2013)
Choi J., Srivastava H.M.: Some summation formulas involving harmonic numbers and generalized harmonic numbers. Math. Comput. Modell. 54, 2220–2234 (2011)
Chu W.: Summation formulae involving harmonic numbers. Filomat 26(1), 143–152 (2012)
Coffey M.W.: On one dimensional digamma and polygamma series related to the evaluation of Feynman diagrams. J. Comput. Appl. Math. 183, 84–100 (2005)
Coffey M.W., Lubbers N.: On generalized harmonic number sums. Appl. Math. Comput. 217, 689–698 (2010)
Flajolet P., Salvy B.: Euler sums and contour integral representations. Exp. Math. 7, 15–35 (1998)
Kölbig K.: The polygamma function \({\psi \left( x\right) }\) for x = 1/4 and x = 3/4. J. Comput. Appl. Math. 75, 43–46 (1996)
Liu H., Wang W.: Harmonic number identities via hypergeometric series and Bell polynomials. Integral Transform. Spec. Funct. 23, 49–68 (2012)
Sitaramachandrarao R.: A formula of S. Ramanujan. J. Number Theory 25, 1–19 (1987)
Sofo A.: Sums of derivatives of binomial coefficients. Adv. Appl. Math. 42, 123–134 (2009)
Sofo A.: Integral forms associated with harmonic numbers. Appl. Math. Comput. 207, 365–372 (2009)
Sofo A.: Integral identities for sums. Math. Commun. 13, 303–309 (2008)
Sofo, A.: Computational Techniques for the Summation of Series. Kluwer Academic/Plenum Publishers, New York (2003)
Sofo, A.: Generalized hypergeometric function identities at argument \({\pm}\) 1. Integral Transform. Spec. Funct. 25, 909–921 (2014)
Sofo A., Srivastava H.M.: Identities for the harmonic numbers and binomial coefficients. Ramanujan J. 25, 93–113 (2011)
Sofo A.: Summation formula involving harmonic numbers. Anal. Math. 379, 51–64 (2011)
Sofo, A.: Second order alternating harmonic number sums. Filomat (2015, in press)
Sofo A.: Quadratic alternating harmonic number sums. J. Number Theory 154, 144–159 (2015)
Srivastava, H.M., Choi, J.: Series Associated with the Zeta and Related Functions. Kluwer Academic Publishers, London (2001)
Srivastava, H.M., Choi, J.: Zeta and q-Zeta Functions and Associated Series and Integrals. Elsevier Science Publishers, Amsterdam (2012)
Wang W., Jia C.: Harmonic number identities via the Newton–Andrews method. Ramanujan J. 35, 263–285 (2014)
Wei C., Gong D.: The derivative operator and harmonic number identities. Ramanujan J. 34, 361–371 (2014)
Zheng D.Y.: Further summation formulae related to generalized harmonic numbers. J. Math. Anal. Appl. 335(1), 692–706 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sofo, A. Identities for Alternating Inverse Squared Binomial and Harmonic Number Sums. Mediterr. J. Math. 13, 1407–1418 (2016). https://doi.org/10.1007/s00009-015-0574-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-015-0574-7