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The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order. (English) Zbl 1237.11009
Summary: This article obtains the multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order and deduces some explicit recursive formulas. The \(\lambda\)-multiple power sum and \(\lambda\)-multiple alternating sum that are clearly evaluated associated with the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, respectively, are also introduced. Some earlier results of Carlitz and Howard can be deduced.

11B68 Bernoulli and Euler numbers and polynomials
05A10 Factorials, binomial coefficients, combinatorial functions
05A15 Exact enumeration problems, generating functions
Full Text: DOI
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