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Theorems on Apostol-Euler polynomials of higher order arising from Euler basis. (English) Zbl 1297.11008
Summary: Recently, D. S. Kim and T. Kim [Integral Transforms Spec. Funct. 24, No. 9, 734–738 (2013; Zbl 1360.11040)] have introduced an useful method to get interesting identities related to Bernoulli and Euler polynomials of higher order. S. Araci et al. [“Theorems on Genocchi polynomials of higher order arising from Genocchi basis”, Preprint] also obtained many interesting equalities related to Genocchi polynomials of higher order arising from Genocchi basis. In this paper, we consider Apostol-Euler polynomials of higher order arising from Euler basis by using the method of Kim. We also try to derive a numerous of interesting properties related to special functions.

MSC:
11B68 Bernoulli and Euler numbers and polynomials
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