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Finite $q$-multiple harmonic sums with one exceptional index
In this paper, we give explicit expressions about $q$-harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices. The case $A=1$ has been extensively studied, and a variety of identities, explicit evaluations, and structural properties are known. Likewise, numerous explicit evaluations are available for $q$
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