The Multiplication Formulas For The Apostol-Bernoulli And Apostol-Euler Polynomials Of Higher Order

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS（2009）

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摘要

This article obtains the multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order and deduces some explicit recursive formulas. The -multiple power sum and -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.

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关键词

Bernoulli numbers and polynomials (of higher order), Apostol-Bernoulli numbers and polynomials (of higher order), Euler numbers and polynomials (of higher order), Apostol-Euler numbers and polynomials (of higher order), Raabe's multiplication formula, multiplication formula, multinomial identity, generalized multinomial identity, power sum and alternating sum, -multiple power sum and -multiple alternating sum

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