대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권2호
  • /
  • Pages.239-255
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  • 2014
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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SHIFTED HARMONIC SUMS OF ORDER TWO

  • 투고 : 2013.09.30
  • 발행 : 2014.04.30
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초록

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

키워드

참고문헌

  1. J. Choi, Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers, J. Ineq. Appl. 49 (2013), 11 p.
  2. J. Choi, Certain summation formulas involving harmonic numbers and generalized harmonic numbers, Appl. Math. Comput. 218 (2011), no. 3, 734-740. https://doi.org/10.1016/j.amc.2011.01.062
  3. J. Choi and D. Cvijovic, Values of the polygamma functions at rational arguments, J. Phys. A: Math. Theor. 40 (2007), no. 50, 15019-15028; Corrigendum, ibidem 43 (2010), no. 23, 239801, 1p. https://doi.org/10.1088/1751-8113/40/50/007
  4. J. Choi and H. M. Srivastava, Some summation formulas involving harmonic numbers and generalized harmonic numbers, Math. Comp. Modelling 54 (2011), no. 9-10, 2220-2234. https://doi.org/10.1016/j.mcm.2011.05.032
  5. W. Chu, Summation formulae involving harmonic numbers, Filomat. 26 (2012), no. 1, 143-152. https://doi.org/10.2298/FIL1201143C
  6. W. Chu, Infinite series identities on harmonic numbers, Results Math. 61 (2012), no. 3-4, 209-221. https://doi.org/10.1007/s00025-010-0089-2
  7. A. Dil and V. Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series II, Appl. Anal. Discrete Math. 5 (2011), no. 2, 212-229. https://doi.org/10.2298/AADM110615015D
  8. H.-T. Jin and L. H. Sun, On Spiess's conjecture on harmonic numbers, Discrete Appl. Math. 161 (2013), no. 13-14, 2038-2041. https://doi.org/10.1016/j.dam.2013.03.024
  9. K. Kolbig, The polygamma function ${\psi}$ (x) for x = 1/4 and x = 3/4, J. Comput. Appl. Math. 75 (1996), no. 1, 43-46.
  10. H. Liu and W. Wang, Harmonic number identities via hypergeometric series and Bell polynomials, Integral Transforms Spec. Funct. 23 (2012), no. 1, 49-68. https://doi.org/10.1080/10652469.2011.553718
  11. E. Munarini, Riordan matrices and sums of harmonic numbers, Appl. Anal. Discrete Math. 5 (2011), no. 2, 176-200. https://doi.org/10.2298/AADM110609014M
  12. A. Sofo, Computational Techniques for the Summation of Series, Kluwer Academic/Plenum Publishers, New York, 2003.
  13. A. Sofo, Sums of derivatives of binomial coefficients, Adv. in Appl. Math. 42 (2009), no. 1, 123-134. https://doi.org/10.1016/j.aam.2008.07.001
  14. A. Sofo, Harmonic sums and integral representations, J. Appl. Anal. 16 (2010), no. 2, 265-277.
  15. A. Sofo, Harmonic number sums in higher powers, J. Math. Anal. 2 (2011), no. 2, 15-22.
  16. A. Sofo, Summation formula involving harmonic numbers, Anal. Math. 37 (2011), no. 1, 51-64. https://doi.org/10.1007/s10476-011-0103-2
  17. A. Sofo, New classes of harmonic number identities, J. Integer Seq. 15 (2012), Article 12.7.4.
  18. A. Sofo, Finite number sums in higher order powers of harmonic numbers, Bull. Math. Anal. Appl. 5 (2013), no. 1, 71-79.
  19. A. Sofo, Mixed binomial sum identities, Integral Transforms Spec. Funct. 24 (2013), no. 3, 187-200. https://doi.org/10.1080/10652469.2012.685937
  20. A. Sofo and H. M. Srivastava, Identities for the harmonic numbers and binomial coefficients, Ramanujan J. 25 (2011), no. 1, 93-113. https://doi.org/10.1007/s11139-010-9228-3
  21. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, London, 2001.

피인용 문헌

  1. Some evaluation of harmonic number sums vol.27, pp.12, 2016, https://doi.org/10.1080/10652469.2016.1231675
  2. Quadratic and cubic harmonic number sums vol.447, pp.1, 2017, https://doi.org/10.1016/j.jmaa.2016.10.026
  3. Some results on q-harmonic number sums vol.2018, pp.1, 2018, https://doi.org/10.1186/s13662-018-1480-7