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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 12, pp. 1587–1603,
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Bedratyuk, L.P. Derivations and Identities for Kravchuk Polynomials. Ukr Math J 65, 1755–1773 (2014). https://doi.org/10.1007/s11253-014-0896-9
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DOI: https://doi.org/10.1007/s11253-014-0896-9