On generalized hyperharmonic numbers of order r, Hn,mr (σ)

被引:1
作者
Koparal, Sibel [1 ]
Omur, Nese [2 ]
Elkhiri, Laid [3 ]
机构
[1] Univ Bursa Uludag, Dept Math, TR-16059 Nilufer, Bursa, Turkiye
[2] Kocaeli Univ, Dept Math, TR-41380 Izmit, Kocaeli, Turkiye
[3] Univ Tiaret, Fac Mat & Sci, Tiaret, Algeria
关键词
Sums; Generalized harmonic numbers; Generating function; IDENTITIES;
D O I
10.7546/nntdm.2023.29.4.804-812
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we define generalized hyperharmonic numbers of order r, H-n,m(r) (sigma), for m is an element of Z(+) and give some applications by using generating functions of these numbers. For example, for n, r, s is an element of Z(+) such that 1 <= s <= r, Sigma(n)(k=1) [GRAPHICS] H-k,m(r-s) (sigma) = H-n,m(r) (sigma), and Sigma(n)(k=1) Sigma(k)(i=1) H-k-i,m(r+1) (sigma) D-r (k - i + r)/(n - k)! (k - i + r)! = H-n,m(2r+2) (sigma), where D-r (n) is an r-derangement number.
引用
收藏
页码:804 / 812
页数:9
相关论文
共 11 条
[1]   THE POLYLOGARITHM IN ALGEBRAIC NUMBER-FIELDS [J].
ABOUZAHRA, M ;
LEWIN, L .
JOURNAL OF NUMBER THEORY, 1985, 21 (02) :214-244
[2]  
Adelberg A., 2002, INT MATH J, V1, P53, DOI 10.1007/978-1-4615-0777-2_4
[3]   Some summation formulas involving harmonic numbers and generalized harmonic numbers [J].
Choi, Junesang ;
Srivastava, H. M. .
MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) :2220-2234
[4]   Binomial sums involving harmonic numbers [J].
Gencev, Marian .
MATHEMATICA SLOVACA, 2011, 61 (02) :215-226
[5]   SUMMATION FORMULAE INVOLVING MULTIPLE HARMONIC NUMBERS [J].
Guo, Dongwei ;
Chu, Wenchang .
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2021, 15 (01) :201-212
[6]   SOME IDENTITIES FOR DERANGEMENT NUMBERS [J].
Koparal, Sibel ;
Omur, Nese ;
Sudemen, Kubra Nur .
MISKOLC MATHEMATICAL NOTES, 2022, 23 (02) :773-785
[7]   Sums involving generalized harmonic and Daehee numbers [J].
Omur, Nese ;
Koparal, Sibel .
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2022, 28 (01) :92-99
[8]  
Ömür N, 2018, ADV APPL MATH SCI, V17, P617
[9]   On the matrices with the generalized hyperharmonic numbers of order r [J].
Omur, Nese ;
Koparal, Sibel .
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2018, 11 (03)
[10]  
SPIESS J, 1990, MATH COMPUT, V55, P839, DOI 10.1090/S0025-5718-1990-1023769-6