Unrestricted Pell and Pell – Lucas 2N-ons

Abstract

In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers. We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons. We give generating functions and Binet formulas for these type of hyper-complex numbers. We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.