Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Jugal Kishore; Vipin Verma

doi:10.17485/IJST/v16i12.2213

Article

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i12.2213

Year: 2023, Volume: 16, Issue: 12, Pages: 941-955

Original Article

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Jugal Kishore^1*, Vipin Verma²

¹Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, 144411, Punjab, India
²SVKM’s Narsee Monjee Institute of Management Studies (NMIMS) University, V.L. Mehta Road, Vile Parle (West) Mumbai, Maharashtra 400056, Mumbai, 400056, Maharashtra

*Corresponding Author
Email: [email protected]

Received Date:19 November 2022, Accepted Date:26 February 2023, Published Date:28 March 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: This study will introduce some new identities for sums of finite products of the Pell, Fibonacci, and Chebyshev polynomials in terms of derivatives of Pell polynomials. Similar identities for Fibonacci and Lucas numbers will be deduced. Methods: Results are obtained by using differential calculus, combinatory computations, and elementary algebraic computations. Findings: In terms of derivatives of Pell polynomials, identities on sums of finite products of the Fibonacci numbers, Lucas numbers, Pell and Fibonacci polynomials, and Chebyshev polynomials of third and fourth kinds are obtained. Novelty: Existing research has identified identities on sums of finite products of the Fibonacci numbers, Lucas numbers, Pell and Fibonacci polynomials, and Chebyshev polynomials of the third and fourth kinds in terms of derivatives of Fibonacci polynomials or Chebyshev polynomials; identities on sums of finite products in terms of Pell polynomials, however, have not been investigated, so identities primarily in terms of Pell polynomials are obtained.

Keywords: Fibonacci Numbers; Pell Numbers; Lucas Numbers; Pell Polynomials; Chebyshev Polynomials

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Copyright

© 2023 Kishore & Verma. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)