Some possible $q$-generalizations of harmonic numbers

Details Some possible $q$-generalizations of harmonic numbers Some possible $q$-generalizations of harmonic numbers

2011-06-24

arxiv.org/abs/1106.5029v1

Mathematics

Combinatorics

Scientific paper

We study three different $q$-analogues of the harmonic numbers. As
applications, we present some generating functions involving number theoretical
functions and give the $q$-generalization of Gosper's exponential generating
function of harmonic numbers. We involve also the $q$-gamma and $q$-digamma
function.

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