Some Identities on Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds

Authors

DOI:

https://doi.org/10.26713/cma.v14i1.2079

Keywords:

Chebyshev polynomials, Pell polynomials, Fibonacci polynomials, Jacobi polynomials, Gegenbauer polynomials, Vieta-Fibonacci polynomials, Vieta-Pell polynomials

Abstract

In this paper, we will introduce some identities involving sums of the finite products of Chebyshev polynomials of the third and fourth kinds, Fibonacci, and Lucas numbers in terms of the derivatives of Pell, Fibonacci, Jacobi, Gegenbauer, Vieta-Fibonacci, Vieta-Pell, and second-kind Chebyshev polynomials.

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References

B. G. S. Doman, The Classical Orthogonal Polynomials, World Scientific Publishing Company, (2015), URL: https://www.perlego.com/book/852001/classical-orthogonal-polynomials-the-pdf.

S. Halici, On the Pell polynomials, Applied Mathematical Sciences 5(37) (2011), 1833 – 1838.

T. Kim, D. S. Kim, D. V. Dolgy and D. Kim, Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds, Advances in Difference Equations 2019 (2019), Article number: 110, DOI: 10.1186/s13662-019-2058-8.

T. Koshy, Pell and Pell-Lucas numbers, in: Pell and Pell-Lucas Numbers with Applications, Springer, pp. 115 – 149, (2014), URL: https://link.springer.com/book/10.1007/978-1-4614-8489-9.

J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, 1st edition, Chapman and Hall/CRC, (2002), DOI: 10.1201/9781420036114.

D. Tasci and F. Yalcin, Vieta-Pell and Vieta-Pell-Lucas polynomials, Advances in Difference Equations 2013 (2013), Article number: 224, DOI: 10.1186/1687-1847-2013-224.

W. Zhang, On Chebyshev polynomials and Fibonacci numbers, Fibonacci Quarterly 40(5) (2002), 424 – 428, URL: https://www.fq.math.ca/Scanned/40-5/zhang-wenpeng.pdf.

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Published

09-05-2023
CITATION

How to Cite

Kishore, J., Verma, V., & Sharma, A. K. (2023). Some Identities on Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Communications in Mathematics and Applications, 14(1), 59–66. https://doi.org/10.26713/cma.v14i1.2079

Issue

Vol. 14 No. 1 (2023)

Section

Research Article

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