Modifiye dejenere Apostol-tipi polinomlar için kesin bağıntılar

Son yıllar da dejenere Bernoulli sayıları, polinomları ve dejenere Euler sayıları, polinomlarını birçok yazarlar tarafından çalışılıyor. Bu makale de modifiye Apostol-Bernoulli polinomları ve modifiye Apostol-Euler polinomlarını tanımladık. Modifiye dejenere Bernoulli polinomları ve modifiye dejenere Euler polinomları için kesin bağıntı verdik. Ayrıca, ikinci çeşit dejenere Stirling sayıları ve modifiye Apostol-Bernoulli polinomları arasında bazı özellikler ispatlandı.

Explicit relations for the modified degenerate Apostol-type polynomials

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.

Keywords:

Bernoulli polynomials and numbers, Euler polynomials and numbers, Modified Bernoulli numbers and polynomials, Modified Euler numbers and polynomials, Degenerate Stirling numbers of the second kind, Degenerate μ-multiple sums Degenerate μ-multiple alternating sums,

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