Derivations and Identities for Kravchuk Polynomials

Abstract

We introduce the notion of Kravchuk derivations of the polynomial algebra. It is proved that any element of the kernel of a derivation of this kind gives a polynomial identity satisfied by the Kravchuk polynomials. In addition, we determine the explicit form of isomorphisms mapping the kernel of the basicWeitzenb¨ock derivation onto the kernels of Kravchuk derivations.