Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials


Kilar N., ŞİMŞEK Y.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.115, no.1, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s13398-020-00968-3
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Chebyshev polynomials, Fibonacci-type polynomials, Trigonometric type polynomials, Hermite-based Milne Thomson type polynomials, Combinatorial sum, Generating function, GENERATING-FUNCTIONS, BERNOULLI
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to give many new and interesting identities, relations, and combinatorial sums including the Hermite-based Milne-Thomson type polynomials, the Chebyshev polynomials, the Fibonacci-type polynomials, trigonometric type polynomials, the Fibonacci numbers, and the Lucas numbers. By using Wolfram Mathematica version 12.0, we give surfaces graphics and parametric plots for these polynomials and generating functions. Moreover, by applying partial derivative operators to these generating functions, some derivative formulas for these polynomials are obtained. Finally, suitable connections of these identities, formulas, and relations of this paper with those in earlier and future studies are designated in detail remarks and observations.