Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

The goal of this study is to develop some new connection formulae between two generalized classes Fibonacci and Lucas polynomials. Hypergeometric functions the kind 2F1(z) are included in all coefficients for a specific z. Several famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, Fermat–Lucas deduced special cases derived formulae. Some introduced generalize those existing literature. As applications formulae, linking celebrated numbers given also newly closed certain definite weighted integrals deduced. Based on using reduction odd even radicals developed.