Abstract:
We investigate multiplication formulas for Apostol-type polynomials and introduce $\lambda$-multiple alternating sums, which are evaluated by Apostol-type polynomials. We derive some explicit recursive formulas and deduce some interesting special cases that involve the classical Raabe formulas and some earlier results of Carlitz and Howard.
Keywords:Apostol-type polynomials, Apostol–Bernoulli numbers and polynomials, Apostol–Euler numbers and polynomials, Apostol–Genocchi numbers and polynomials, multinomial identity, generalized multinomial identity, recursive formula, Raabe's multiplication formula, alternating sum, $\lambda$-multiple alternating sum.
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