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Some Results for Generalized Harmonic Numbers
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Cong-Jiao Feng
Published/Copyright:
November 25, 2009
Abstract
In this paper, we discuss the properties of a class of generalized harmonic numbers H(n, r). By means of the method of coefficients, we establish some identities involving H(n, r). We obtain a pair of inversion formulas. Furthermore, we investigate certain sums related to H(n, r), and give their asymptotic expansions. In particular, we obtain the asymptotic expansion of certain sums involving H(n, r) and the inverse of binomial coefficients by Laplace's method.
Received: 2007-07-08
Revised: 2009-06-13
Accepted: 2009-08-04
Published Online: 2009-11-25
Published in Print: 2009-November
© de Gruyter 2009
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- Counting Determinants of Fibonacci–Hessenberg Matrices Using LU Factorizations
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- On the Kernel of the Coprime Graph of Integers
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Keywords for this article
Harmonic numbers;
Cauchy numbers;
associated Stirling numbers;
asymptotic expansion
Articles in the same Issue
- An Analogue of the Erdős–Ginzburg–Ziv Theorem for Quadratic Symmetric Polynomials
- Counting Determinants of Fibonacci–Hessenberg Matrices Using LU Factorizations
- A Short Proof of a Series Evaluation in Terms of Harmonic Numbers
- Generalization of an Identity Involving the Generalized Fibonacci Numbers and Its Applications
- Inductive Methods and Zero-Sum Free Sequences
- On the Number of Zero-Sum Subsequences of Restricted Size
- On the Average Asymptotic Behavior of a Certain Type of Sequence of Integers
- On the Kernel of the Coprime Graph of Integers
- Bell Numbers and Variant Sequences Derived from a General Functional Differential Equation
- Balanced Subset Sums in Dense Sets of Integers
- Some Results for Generalized Harmonic Numbers
