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Combinatorial Identities on \(q\)-Harmonic Numbers

Wenchang Chu1, Qinglun Yan2
1Dipartimento di Matematica, Universita del Salento Lecce-Arnesano P. OQ. Box 193, Lecce 73100, Italy
2College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210046, P. R. China

Abstract

By means of the \( q \)-finite differences and the derivative operator, we derive, from an alternating \( q \)-binomial sum identity with a free variable \( x \), several interesting identities concerning the generalized \( q \)-harmonic numbers.