论文标题
两种普遍类的斐波那契和卢卡斯多项式的新结果及其在减少某些自由基中的用途
Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals
论文作者
论文摘要
本文关注的是在两个通用类的斐波那契和卢卡斯多项式之间开发一些新的连接公式。对于某些$ z $，所有连接系数都涉及类型$ _2F_ {1}（z）$的超几何功能。一些著名多项式之间的几个新连接公式，例如斐波那契，卢卡斯，佩尔，费玛，佩尔 - 卢卡斯和费玛 - 卢卡斯多项式，被推导为派生连接公式的特殊情况。一些引入的公式概括了文献中存在的一些。作为派生连接公式的两个应用，给出了一些链接一些著名数字的新公式，还推导了某些确定的加权积分的新封闭公式。基于使用两种广义类的斐波那契和卢卡斯多项式，开发了某些奇数甚至自由基的一些新的还原公式。
This paper is concerned with developing some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. All the connection coefficients involve hypergeometric functions of the type $_2F_{1}(z)$, for certain $z$. Several new connection formulae between some famous polynomials such as Fibonacci, Lucas, Pell, Fermat, Pell-Lucas, and Fermat-Lucas polynomials are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed.
