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arXiv · 0710.5681

q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions

Yilmaz Simsek
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Abstract

The aim of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, q-analogue Genocchi type l-function and two-variable q-Genocchi type l-function. Furthermore, we construct new genereting functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations related to q-Hardy-Berndt type sums and q-Genocchi zeta function as well.

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Yilmaz Simsek. 2007-10-30. q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions. https://doi.org/10.1016/j.na.2008.11.014

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