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Identities in the spirit of Eule

  • A. Sofo [1]
    1. [1] Victoria University

      Victoria University

      Australia

  • Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 35, Nº 1, 2020, págs. 21-34
  • Idioma: inglés
  • DOI: 10.17398/2605-5686.35.1.21
  • Enlaces
  • Resumen
    • In this paper we develop new identities in the spirit of Euler. We shall investigate and report on new Euler identities of weight p+ 2, for p an odd integer, but with a non unitary argument of the harmonic numbers. Some examples of these Euler identities will be given in terms of Riemann zeta values, Dirichlet values and other special functions

  • Referencias bibliográficas
    • [1] Borwein, D.; Borwein, J. M..; Girgensohn, R. Explicit evaluation of Euler sums. Proc. Edinburgh Math. Soc. (2) 38 (1995), no. 2, 277–294.
    • [2] Bailey, D. H. Borwein, J. M. Computation and structure of character polylogarithms with applications to character Mordell-TornheimWitten...
    • [3] Choi, Junesang Log-sine and log-cosine integrals. Honam Math. J. 35 (2013), no. 2, 137–146.
    • [4] Devoto, A. Duke, D. W. Table of integrals and formulae for Feynman diagram calculations. Riv. Nuovo Cimento (3) 7 (1984), no. 6, 1–39.
    • [5] Euler, L. Meditationes circa singulare serierum genus, Novi Comm. Acad. Sci. Petropol. 20 (1776), 140-186; reprinted in Opera Omnia, Ser....
    • [6] Flajolet, P. Salvy, B. Euler sums and contour integral representations. Experiment. Math. 7 (1998), no. 1, 15–35.
    • [7] Freitas, P. Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums. Math. Comp. 74 (2005), no. 251, 1425– 1440.
    • [8] Hoffman, M. E., Multiple harmonic series, Pacific J. Math. 152 (1992), 275-290.
    • [9] K¨olbig, K. S. Nielsen’s generalized polylogarithms. SIAM J. Math. Anal. 17 (1986), no. 5, 1232–1258.
    • [10] Lewin, R. Polylogarithms and Associated Functions. North Holland, New York, 1981.
    • [11] Markett, C. Triple sums and the Riemann zeta function. J. Number Theory 48 (1994), no. 2, 113–132.
    • [12] Sitaramachandra Rao, R. A formula of S. Ramanujan. J. Number Theory 25 (1987), no. 1, 1–19.
    • [13] Sofo, A. Polylogarithmic connections with Euler sums. Sarajevo J. Math. 12(24) (2016), no. 1, 17–32.
    • [14] Sofo, A. Integrals of logarithmic and hypergeometric functions. Commun. Math. 24 (2016), no. 1, 7–22.
    • [15] Sofo, A. and Cvijovi´c, D. Extensions of Euler Harmonic Sums, Appl. Anal. Discrete Math. 6 (2012), 317–328.
    • [16] Sofo, A. Integrals of inverse trigonometric and polylogarithmic functions. Submitted, 2019.
    • [17] Sofo, A.; Srivastava, H. M. A family of shifted harmonic sums. Ramanujan J. 37 (2015), no. 1, 89–108.
    • [18] Sofo, A. New classes of harmonic number identities. J. Integer Seq. 15 (2012), no. 7, Article 12.7.4, 12 pp.
    • [19] Sofo, A. Families of Integrals of Polylogarithmic Functions, Special Functions and Applications. Editors Choi, J. and Shilin, I. Mathematics (2019),...
    • [20] Xu, Ce. Yan, Yuhuan. Shi, Zhijuan. Euler sums and integrals of polylogarithm functions. J. Number Theory 165 (2016), 84–108.
    • [21] Zagier, D. Values of zeta functions and their applications, in First European Congress of Mathematicians, Vol II (Paris, 1992), Birkhauser, Boston,...

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