Abstract
Recently, the degenerate Bernoulli numbers and polynomials and the degenerate Euler numbers and polynomials have been studied by several authors. In this paper, we consider the modified Apostol-Bernoulli polynomials and the modified Apostol-Euler polynomials. We give explicit relation for the modified degenerate Bernoulli polynomials and the modified degenerate Euler polynomials. Also, we prove some identities between the modified Apostol-Bernoulli polynomials and the degenerate Stirling numbers of two kinds.
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