A new \(q\)-analogue of Bernoulli polynomials associated with \(p\)-adic \(q\)-integrals. (English) Zbl 1217.11116

Summary: We study a new \(q\)-analogue of Bernoulli polynomials associated with \(p\)-adic \(q\)-integrals. Furthermore, we examine the Hurwitz-type \(q\)-zeta functions, replacing \(p\)-adic rational integers \(x\) with a \(q\)-analogue \([x]_{q}\) for a \(p\)-adic number \(q\) with \(|q - 1|_p<1\), which interpolate \(q\)-analogue of Bernoulli polynomials.


11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
11B68 Bernoulli and Euler numbers and polynomials
11S40 Zeta functions and \(L\)-functions
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