%0 Journal Article
%T On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices
%A Mama Foupouagnigni
%A Salifou Mboutngam
%J -
%D 2019
%R https://doi.org/10.3390/axioms8020047
%X Abstract In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, difference or q-difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the divided-difference operator as well as by defining explicitly, the right and the ¡°left¡± inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution¡ªnon polynomial solution¡ªof a second-order divided-difference equation of hypergeometric type. View Full-Tex
%K second-order differential/difference/q-difference equation of hypergeometric type
%K non-uniform lattices
%K divided-difference equations
%K polynomial solution
%U https://www.mdpi.com/2075-1680/8/2/47