Abstract

The main object of the current paper is to introduce and investigate a new unified class of the degenerate Apostol-type polynomials. These polynomials are studied by means of the generating function, series definition and are framed within the context of monomiality principle. Several important recurrence relations and explicit representations for the antecedent class of polynomials are derived. As the special cases, the degenerate Apostol–Bernoulli, Euler and Genocchi polynomials are obtained and corresponding results are also proved. A fascinating example is constructed in terms of truncated-exponential polynomials, which gives the applications of these polynomials to produce their hybridized forms.

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