Some results on q-harmonic number sums

被引:1
|
作者
Si, Xin [1 ]
机构
[1] Xiamen Univ Technol, Sch Appl Math, Xiamen, Peoples R China
关键词
q-harmonic number; q-binomial coefficient; q-polylogarithm function; Q-ZETA FUNCTIONS; EULER SUMS; INTEGRAL-REPRESENTATIONS; Q-ANALOGS; IDENTITIES; POLYNOMIALS; VALUES; SERIES;
D O I
10.1186/s13662-018-1480-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit formulas for several classes of q-harmonic sums in terms of q-polylogarithms and q-harmonic numbers. The given representations are new.
引用
收藏
页数:16
相关论文
共 50 条
  • [11] IDENTITY ON q-HARMONIC NUMBER RELATED TO PARTIAL BELL POLYNOMIALS
    Yan, Qinglun
    Liu, Yaqing
    Fan, Xiaona
    UTILITAS MATHEMATICA, 2016, 100 : 193 - 200
  • [12] Q-harmonic functions in hyperspace
    Humbert, P
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1926, 182 : 1262 - 1264
  • [13] A REALIZATION OF THE Q-HARMONIC OSCILLATOR
    ATAKISHIEV, NM
    SUSLOV, SK
    THEORETICAL AND MATHEMATICAL PHYSICS, 1991, 87 (01) : 442 - 444
  • [14] Some evaluation of harmonic number sums
    Xu, Ce
    Zhang, Mingyu
    Zhu, Weixia
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (12) : 937 - 955
  • [15] ELEMENTS OF Q-HARMONIC ANALYSIS
    FEINSILVER, P
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 141 (02) : 509 - 526
  • [16] Remarks on irrationality of q-harmonic series
    Wadim Zudilin
    manuscripta mathematica, 2002, 107 : 463 - 477
  • [17] The q-harmonic oscillator in a lattice model
    van Leeuwen, H
    Maassen, H
    JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (12) : 6424 - 6440
  • [18] On q-Laplace operator and q-harmonic polynomials
    N. Z. Iorgov
    A. U. Klimyk
    Physics of Atomic Nuclei, 2001, 64 : 2131 - 2135
  • [19] Remarks on irrationality of q-harmonic series
    Zudilin, W
    MANUSCRIPTA MATHEMATICA, 2002, 107 (04) : 463 - 477
  • [20] On q-Laplace operator and q-harmonic polynomials
    Iorgov, NZ
    Klimyk, AU
    PHYSICS OF ATOMIC NUCLEI, 2001, 64 (12) : 2131 - 2135