Binomial summation formulas involving Pell and Pell–Lucas polynomials

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-03-14 DOI:10.1007/s13324-025-01045-x

Yulei Chen, Yanan Zhao, Dongwei Guo

引用次数: 0

Abstract

By employing two fundamental binomial transformation formulae, several binomial summation formulas involving Pell and Pell-Lucas polynomials are established. Notably, specific instances of these formulas yield intriguing identities involving Fibonacci/Lucas and Pell/Pell-Lucas numbers. In particular, this work offers innovative proofs for two identities introduced by Ohtsuka and Tauraso (2020), as well as a problem posed by Seiffert in 1995.

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通过使用两个基本二项式变换公式，建立了涉及佩尔和佩尔-卢卡斯多项式的几个二项式求和公式。值得注意的是，这些公式的具体实例产生了涉及斐波那契/卢卡斯数和佩尔/佩尔-卢卡斯数的耐人寻味的等式。特别是，这项工作为 Ohtsuka 和 Tauraso（2020 年）提出的两个等式以及 Seiffert 于 1995 年提出的一个问题提供了创新证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.