On some identities and generating functions for Pell-Lucas numbers

Abstract

Generating functions for Pell and Pell-Lucas numbers are obtained. Applications are given for some results recently obtained by Mansour [Mansour12]; by using an alternative approach that considers the action of the operator ${\delta }_{e_1{e}_2}^k$ to the series $\sum _{j=0}^{\mathrm{\infty }}{a}_j(e_{1}z{)}^j$.