On computational formulas for parametric type polynomials and its applications

Abstract

In this paper, many formulas and identities for computing the r-parametric Hermite type polynomials are given with the help of generating functions. Using generating functions and algebraic methods, a relation is also given including these polynomials and the 2-variable Hermite Kampé de Fériet polynomials. Moreover, many relations and formulas containing the two parametric type of Apostol-Bernoulli polynomials of higher order, the two parametric type of Apostol-Euler polynomials of higher order, the two parametric type of Apostol-Genocchi polynomials of higher order and the Dickson polynomials are obtained. Finally, some special values of these polynomials and their applications with trigonometric functions are presented.

Keywords

• Hermite type polynomials
• Apostol type numbers and polynomials
• parametric type polynomials
• special numbers and polynomials
• generating functions

Parametrik tip polinomlar için hesaplama formülleri ve uygulamaları

Abstract

Bu çalışmada, r-parametreli Hermite tipli polinomların hesaplanması için birçok formüller ve bağıntılar, üreteç fonksiyonları yardımıyla verilmiştir. Üreteç fonksiyonları ve cebirsel yöntemler kullanılarak, bu polinomları ve 2-değişkenli Hermite Kampé de Fériet polinomlarını içeren bir bağıntı da verilmiştir. Ayrıca, yüksek mertebeden iki parametreli Apostol-Bernoulli polinomları, yüksek mertebeden iki parametreli Apostol-Euler polinomları, yüksek mertebeden iki parametreli Apostol-Genocchi polinomları ve Dikson polinomlarını içeren birçok bağıntılar ve formüller elde edilmiştir. Son olarak, bu polinomların bazı özel değerleri ve trigonometrik fonksiyonlarla uygulamaları sunulmuştur.

Keywords

• Hermite tipli polinomlar
• Apostol tipli sayılar ve polinomlar
• parametrik tipli polinomlar
• özel sayılar ve polinomlar
• üreteç fonksiyonları

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