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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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.

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Acknowledgements

The paper was supported by Scientific Research Project Administration of Akdeniz University with Project Number: FDK-2020-5276. Due to some suggested references and also suggestions, the authors would like to thank all referees for their valuable comments.

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  1. Department of Mathematics, Faculty of Science, University of Akdeniz, 07058, Antalya, Turkey

    Neslihan Kilar & Yilmaz Simsek

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  1. Neslihan Kilar
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  2. Yilmaz Simsek
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Correspondence to Neslihan Kilar.

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Kilar, N., Simsek, Y. Identities and relations for Hermite-based Milne–Thomson polynomials associated with Fibonacci and Chebyshev polynomials. RACSAM 115, 28 (2021). https://doi.org/10.1007/s13398-020-00968-3

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