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BY 4.0 license Open Access Published by De Gruyter Open Access January 19, 2021

On identities involving generalized harmonic, hyperharmonic and special numbers with Riordan arrays

  • Sibel Koparal EMAIL logo , Neşe Ömür and Ömer Duran
From the journal Special Matrices

Abstract

In this paper, by means of the summation property to the Riordan array, we derive some identities involving generalized harmonic, hyperharmonic and special numbers. For example, for n ≥ 0,

k=0nBkk!H(n.k,α)=αH(n+1,1,α)-H(n,1,α),

and for n > r ≥ 0,

k=rn-1(-1)ks(k,r)r!αkk!Hn-k(α)=(-1)rH(n,r,α),

where Bernoulli numbers Bn and Stirling numbers of the first kind s (n, r).

MSC 2010: 11B99; 11C20; 15A23

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Received: 2020-05-25
Accepted: 2020-12-15
Published Online: 2021-01-19

© 2021 Sibel Koparal et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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