On computational formulas for parametric type polynomials and its applications

Year 2023, Volume: 25 Issue: 1, 13 - 30, 16.01.2023

Neslıhan Kılar

https://doi.org/10.25092/baunfbed.1083754

Cited By: 1

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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