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A note on the multiple twisted Carlitz’s type \(q\)-Bernoulli polynomials. (English) Zbl 1195.11029

Summary: We give the twisted Carlitz’s type \(q\)-Bernoulli polynomials and numbers associated with \(p\)-adic \(q\)-integrals and discuss their properties. Furthermore, we define the multiple twisted Carlitz’s type \(q\)-Bernoulli polynomials and numbers and obtain the distribution relation for them.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33E50 Special functions in characteristic \(p\) (gamma functions, etc.)
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References:

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