Publication: Some identities with multi-generalized q -hyperharmonic numbers of order r
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Koparal, Sibel
Authors
Chen, Zhihua
Ömür, Neşe
Khan, Waseem Ahmad
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Mdpi
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Abstract
The main purpose of this paper is to define multiple alternative q-harmonic numbers, H-n(k; q) and multi-generalized q-hyperharmonic numbers of order r, H-n(r) (k; q) by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms Li-q; k1,Li-k2,Li-...,Li-kd (t(1), t(2),...,t(d)) with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.
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Keywords
Zeta-values, Duality, Symmetry, Q-multiple zeta values, Q-analogue of multiple polylogaritms, Multi-generalized q-hyperharmonic numbers of order r, Q-series, Science & technology, Multidisciplinary sciences, Science & technology - other topics