On analogous representations for the Apostol-Euler polynomials and numbers of higher order
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Inspired by explicit hypergeometric representations of higher-order Apostol–Euler polynomials, a promis ing direction in the study of special polynomials is the development of an expansion framework for fami lies of Apostol-type polynomials by means of hypergeometric function structures. This perspective seeks to extend the known connections between Gaussian hypergeometric functions and polynomial generating functions by introducing a parameterized approach that includes Apostol–Bernoulli and Apostol–Euler polynomials. The algebraic and combinatorial implications of these expansions may lead to the discovery of new identities, recurrence relations, and transformation formulas.
