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Finite Mixed Sums wih Harmonic Terms

  • Anthony Sofo EMAIL logo
From the journal Mathematica Slovaca


In the spirit of Euler sums we develop a set of identities for finite sums of products of harmonic numbers in higher order and reciprocal binomial coefficients. The new results complement some Euler sums of the type


[1] CHEON, G. S.-EL-MIKKAWY, M. E. A.: Generalized harmonic numbers with Riordan arrays, J. Number Theory 128 (2008), 413-425.10.1016/j.jnt.2007.08.011Search in Google Scholar

[2] CHOI, J.: Certain summation formulas involving harmonic numbers and generalized harmonic numbers, Appl. Math. Comput. (2011), doi:10.1016/j.amc.2011. in Google Scholar

[3] GENČEV, M.: Binomial sums involving harmonic numbers, Math. Slovaca. 61 (2011), 215-226.10.2478/s12175-011-0006-5Search in Google Scholar

[4] HE, T. X.-HU, L. C.-YIN, D.: A pair of summation formulas and their applications, Comput. Math. Appl. 58 (2009), 1340-1348.10.1016/j.camwa.2009.07.033Search in Google Scholar

[5] KRONENBURG, M. J.: Some combinatorial identities some of which involving harmonic numbers, http://arXiv.1103.1268V1 (2011).Search in Google Scholar

[6] KUBA, M.-PRODINGER, H.-SCHNEIDER, C.: Generalized reciprocity laws for sums of harmonic numbers, Integers 8 (2008), A17.Search in Google Scholar

[7] OSBURN, R.-SCHNEIDER, C.: Gaussian hypergeometric series and supercongruences, Math. Comp. 78 (2009), 275-292.10.1090/S0025-5718-08-02118-2Search in Google Scholar

[8] PRODINGER, H.: Identities involving harmonic numbers that are of interest to physicists, Util. Math. 83 (2010), 291-299.Search in Google Scholar

[9] SOFO, A.-SRIVASTAVA, H. M.: Identities for the harmonic numbers and binomial coefficients, Ramanujan J. 25 (2011), 93-113.10.1007/s11139-010-9228-3Search in Google Scholar

[10] SOFO, A.: Computational Techniques for the Summation of Series, Kluwer Academic/ Plenum Publishers, New York, 2003.10.1007/978-1-4615-0057-5Search in Google Scholar

[11] SOFO, A.: Sums of derivatives of binomial coefficients, Adv. Appl. Math. 42 (2009), 123-134.10.1016/j.aam.2008.07.001Search in Google Scholar

[12] SOFO, A.: Summation formula involving harmonic numbers, Anal. Math. 37 (2011), 51-64.10.1007/s10476-011-0103-2Search in Google Scholar

[13] SOFO, A.: Harmonic sums and integral representations, J. Appl. Anal. 16 (2010), 265-277.10.1515/jaa.2010.018Search in Google Scholar

[14] SOFO, A.: Finite sums in higher order powers of harmonic numbers, J. Math. Anal. 2 (2011), 15-22.Search in Google Scholar

[15] SRIVASTAVA, R.: Some families of combinatorial and other series identities and their applications, Appl. Math. Comput. (2011), doi:10.1016/j.amc.2010. in Google Scholar

[16] WANG, W.: Riordan arrays and harmonic number identities, Comput. Math. Appl. 60 (2010), 1494-1509.10.1016/j.camwa.2010.06.031Search in Google Scholar

[17] WANG, X.-LI, M.: Dixon’s formula and identities involving harmonic numbers, J. Integer Seq. 14 (2011), Article 11.1.3.Search in Google Scholar

[18] ZHENG, D. Y.: Further summation formulae related to generalized harmonic numbers, J. Math. Anal. Appl. 335 (2007), 692-706. 10.1016/j.jmaa.2007.02.002Search in Google Scholar

Received: 2012-6-11
Accepted: 2012-12-13
Published Online: 2015-12-9
Published in Print: 2015-10-1

Mathematical Institute Slovak Academy of Sciences

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