Generalized harmonic numbers with Riordan arrays

被引：43

作者：

Cheon, Gi-Sang ^{[1
]}

El-Mikkawy, M. E. A. ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[2] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

JOURNAL OF NUMBER THEORY | 2008年 / 128卷 / 02期

关键词：

Harmonic numbers; Stirling numbers; Riordan array; Symmetric polynomial; Harmonic polynomial; Bernoulli polynomial;

D O I：

10.1016/j.jnt.2007.08.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By observing that the infinite triangle obtained from some generalized harmonic numbers follows a Riordan array, we obtain very simple connections between the Stirling numbers of both kinds and other generalized harmonic numbers. Further, we suggest that Riordan arrays associated with such generalized harmonic numbers allow us to find new generating functions of many combinatorial sums and many generalized harmonic number identities. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：413 / 425

页数：13

共 12 条

[1]

Abramowitz M., 1970, HDB MATH FUNCTIONS

[2] On Stirling numbers and Euler sums [J].

Adamchik, V .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 79 (01) :119-130

[3] The multiple gamma function and its application to computation of series [J].

Adamchik, VS .

RAMANUJAN JOURNAL, 2005, 9 (03) :271-288

[4]

[Anonymous], 2003, INTEGERS

[5] Harmonic number identities and Hermite-Pade approximations to the logarithm function [J].

Chu, W .

JOURNAL OF APPROXIMATION THEORY, 2005, 137 (01) :42-56

[6]

Gertsch A, 1997, CR ACAD SCI I-MATH, V324, P7

[7] On Miki's identity for Bernoulli numbers [J].

Gessel, IM .

JOURNAL OF NUMBER THEORY, 2005, 110 (01) :75-82

[8] On some alternative characterizations of Riordan arrays [J].

Merlini, D ;

Rogers, DG ;

Sprugnoli, R ;

Verri, MC .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1997, 49 (02) :301-320

[9] PASCAL TRIANGLES, CATALAN NUMBERS AND RENEWAL ARRAYS [J].

ROGERS, DG .

DISCRETE MATHEMATICS, 1978, 22 (03) :301-310

[10] A Stirling like sequence of rational numbers [J].

Santmyer, JM .

DISCRETE MATHEMATICS, 1997, 171 (1-3) :229-235

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