Some Convolution Formulae Related to the Second-Order Linear Recurrence Sequence

@article{Chen2019SomeCF,
title={Some Convolution Formulae Related to the Second-Order Linear Recurrence Sequence},
author={Zhuoyu Chen and Lan Qi},
journal={Symmetry},
year={2019},
volume={11},
pages={788}
}

The main aim of this paper is that for any second-order linear recurrence sequence, the generating function of which is f ( t ) = 1 1 + a t + b t 2 , we can give the exact coefficient expression of the power series expansion of f x ( t ) for x ∈ R with elementary methods and symmetry properties. On the other hand, if we take some special values for a and b, not only can we obtain the convolution formula of some important polynomials, but also we can establish the relationship between… Expand