217
Views
2
CrossRef citations to date
0
Altmetric
Research Articles

Infinite series involving harmonic numbers of convergence rate 1/2

Pages 570-590 | Received 22 Jul 2021, Accepted 01 Nov 2021, Published online: 19 Nov 2021

References

  • Bailey WN. Generalized hypergeometric series. Cambridge: Cambridge University Press; 1935.
  • Boyadzhiev KN. Series with central binomial coefficients, Catalan numbers, and harmonic numbers. J Integer Seq. 2012;15. Art#12.1.7.
  • Chu W. Inversion techniques and combinatorial identities: a unified treatment for the 7F6-series identities. Collect Math. 1994;45(1):13–43.
  • Gessel I. Finding identities with the WZ method. J Symbolic Comput. 1995;20(5/6):537–566.
  • Ekhad SB. Forty strange computer-discovered and computer-proved (of course) hypergeometric series evaluations. Available from: http://www.math.rutgers.edu/zeilberg/ekhad/ekhad.html.
  • Chen X, Chu W. Dixon's 3F2(1)-series and identities involving harmonic numbers and Riemann zeta function. Discrete Math. 2010;310(1):83–91.
  • Chu W. Hypergeometric series and the Riemann zeta function. Acta Arith. 1997;82(2):103–118.
  • Chu W. Hypergeometric approach to Apéry-like series. Integr Trans Spec Funct. 2017;28(7):505–518.
  • Chu W, Campbell JM. Harmonic sums from the Kummer theorem. J Math Anal Appl. 2021;501. Art#125179.
  • Chu W, DeDonno L. Hypergeometric series and harmonic number identities. Adv Appl Math. 2005;34(1):123–137.
  • Liu H, Wang WP. Harmonic number identities via hypergeometric series and Bell polynomials. Integr Trans Spec Funct. 2012;23(1):49–68.
  • Liu H, Zhou W, Ding S. Generalized harmonic number summation formulae via hypergeometric series and digamma functions. J Differ Equ Appl. 2017;23(7):1204–1218.
  • Tauraso R. Supercongruences related to 3F2(1) involving harmonic numbers. Int J Number Theory. 2018;14(4):1093–1109.
  • Wang XY, Chu W. Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients. Ramanujan J. 2020;52(3):641–668.
  • Campbell JM. Ramanujan-like series for 1π involving harmonic numbers. Ramanujan J. 2018;46(2):373–387.
  • Campbell JM. New series involving harmonic numbers and squared central binomial coefficients. Rocky Mountain J Math. 2019;49(8):2513–2544.
  • Campbell JM, D'Aurizio J, Sondow J. On the interplay among hypergeometric functions. Complete elliptic integrals, and Fourier–Legendre expansions. J Math Anal Appl. 2019;479(1):90–121.
  • Chen H. Interesting series associated with central binomial coefficients, Catalan numbers and harmonic numbers. J Integer Seq. 2016;19. Art#16.1.5.
  • Chu W. Analytical formulae for extended 3F2-series of Watson–Whipple–Dixon with two extra integer parameters. Math Comp. 2012;81(277):467–479.
  • Rainville ED. Special functions. New York (NY): Macmillan; 1960.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.