## 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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