An explicit Formula for Bernoulli Polynomials with a q Parameter in Terms of r-Whitney Numbers
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polynomialsbernoullinumbersparametertermswhitneyalgebraiccauchy
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We define the Bernoulli polynomials with a $q$ parameter in terms of $r$-Whitney numbers of the second kind. Some algebraic properties and combinatorial identities of these polynomials are given. Also, we obtain several relations between the Cauchy and Bernoulli polynomials with a $q$ parameter in terms of $r$-Whitney numbers of both kinds.
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