Near-legendre differential equations

Abstract EN

A differential equation of the form (( ) ) integers is called a near-Legendre equation.

We show that such an equation has infinitely many polynomial solutions corresponding to infinitely many λ.

We list all of these equations for .

We show, for , that these solutions are 'partially' orthogonal with respect to some weight functions and show how to expand functions using these polynomials.

We give few applications to partial differential equations