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Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. (English) Zbl 1189.11011

The author defines the Apostol-Euler polynomials of higher order, and establishes some elementary properties of these polynomials. For example, the author obtains several explicit formulas involving the Gaussian hypergeometric functions and the Stirling numbers of the second kind.
Reviewer: Hao Pan (Nanjing)

MSC:

11B68 Bernoulli and Euler numbers and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B73 Bell and Stirling numbers
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