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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.

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