• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.231-242
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• 2013

In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.