Reciprocal Formulae among Pell and Lucas Polynomials

Mei Bai, Wenchang Chu and Dongwei Guo
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Mei Bai: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Wenchang Chu: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Dongwei Guo: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

Mathematics, 2022, vol. 10, issue 15, 1-11

Abstract: Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Lucas numbers.

Keywords: generating function; Lambert series; bisection series; reciprocal relation; binomial coefficient; Fibonacci and Lucas numbers; Pell and Lucas polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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