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p-Bernoulli and geometric polynomials

    https://doi.org/10.1142/S1793042118500665Cited by:7 (Source: Crossref)

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

    AMSC: 11B68, 11B83
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