Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients

Guo, Dongwei

doi:10.47443/dml.2021.0090

Discrete Math. Lett.

2021

DOI: 10.47443/dml.2021.0090

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Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients

Dongwei Guo¹

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2024

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q-Abel-Zeilberger Algorithm and q-Hyperharmonic Numbers Identities

周

2024

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q-Abel-Zeilberger Algorithm and q-Hyperharmonic Numbers Identities

周

2024

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Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

Cereceda¹

2022

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In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling polynomials of the first kind and show the relationship between the (exponential) complete Bell polynomials and the r-Stirling numbers of the first kind. Furthermore, we provide a new formula for obtaining the generalized Bernoulli polynomials by exploiting their link with the higher-order derivatives of the hyperharmonic polynomials. In addition, we obtain various identities involving the r-Stirling numbers of the first kind, the Bernoulli numbers and polynomials, the Stirling numbers of the first and second kind, and the harmonic numbers.

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Identities on q-Harmonic Numbers

Zhou,

Jin,

Zheng

2024

JAMP

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Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients

Cited by 3 publications

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<i>q</i>-Abel-Zeilberger Algorithm and <i>q</i>-Hyperharmonic Numbers Identities

<i>q</i>-Abel-Zeilberger Algorithm and <i>q</i>-Hyperharmonic Numbers Identities

Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

Identities on <i>q</i>-Harmonic Numbers

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Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients

Cited by 3 publications

References 0 publications

<i>q</i>-Abel-Zeilberger Algorithm and <i>q</i>-Hyperharmonic Numbers Identities

<i>q</i>-Abel-Zeilberger Algorithm and <i>q</i>-Hyperharmonic Numbers Identities

Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

Identities on &lt;i&gt;q&lt;/i&gt;-Harmonic Numbers

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Identities on <i>q</i>-Harmonic Numbers