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An analogue of the zeta function and its applications. (English) Zbl 1112.11013
Summary: We construct new analogues of Bernoulli numbers and polynomials. We define the $$q$$-extension of zeta function. Finally we give relation between the $$q$$-extension of zeta functions and the $$(h,q)$$-extension of Bernoulli polynomials.

##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 11S40 Zeta functions and $$L$$-functions 33B30 Higher logarithm functions 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$
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##### References:
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