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

来源：

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2023年 / 29卷 / 04期

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

页码：804 / 812

页数：9

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