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

Zhuoyu Chen, Lan Qi
2019 Symmetry  
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
more » ... between polynomials and themselves. For example, we can find relationship between the Chebyshev polynomials and Legendre polynomials.
doi:10.3390/sym11060788 fatcat:ndkvprunxbh7ni4erhr3ry3qgq