Families of Legendre–Sheffer polynomials

In this paper, we introduce families of Legendre–Sheffer polynomials corresponding to two different forms of 2-variable Legendre polynomials. We discuss their special properties and establish a correspondence between the Sheffer and Legendre–Sheffer families. Further, we obtain some important results involving Legendre-Hermite and Legendre-Laguerre polynomials as applications.