-Bernoulli and geometric polynomials
Abstract
We relate geometric polynomials and -Bernoulli polynomials with an integral representation, then obtain several properties of -Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of -Bernoulli polynomials. Finally, we introduce poly--Bernoulli polynomials and numbers, then study some arithmetical and number theoretical properties of them.
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