Derivations and Identities for Kravchuk Polynomials
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 12, pp 1755-1773.
Citation Example: Bedratyuk L. P. Derivations and Identities for Kravchuk Polynomials // Ukr. Mat. Zh. - 2013. - 65, № 12. - pp. 1587–1603.