arXiv subjects

Jinfa Cheng

Publications and source records attributed to Jinfa Cheng.

3 recordsLinked to original sources

arXiv2020

Adjoint Difference Equation for a Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on Non-uniform Lattices

In this article, we establish the adjoint equation for Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on non-uniform lattices, and prove it to be a difference equation of hypergeometric type on non-uniform lattices as well. The particular solutions of the adjoint equation are then obtained. As an appliction of these particular solutions, we use them to obtain the particular solutions for the original difference equation of hypergeometric type on non-uniform lattices. Finally, we prove another kind of fundamental theorems for Nikiforov-Uvarov-Suslov difference equation of hypergeometric type, which are essentially new results, its expression is different from Suslov's Theorem.

math.CA↗

arXiv2019

On the Definitions of Fractional Sum and Difference on Non-uniform Lattices

As is well known, the idea of a fractional sum and difference on uniform lattice is more current, and gets a lot of development in this field. But the definitions of fractional sum and fractional difference of $f(z)$ on non-uniform lattices $x(z)=c_{1}z^{2}+c_{2}z+c_{3}$ or $x(z)=c_{1}q^{z}+c_{2}q^{-z}+c_{3}$ seem much more difficult and complicated. In this article, for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways. The analogue of Euler's Beta formula, Cauchy' Beta formula on on non-uniform lattices are established, and some fundamental theorems of fractional calculas, the solution of the generalized Abel equation and fractional central difference equations on non-uniform lattices are obtained etc.

math.CA↗

arXiv2018

Generalizations of Rodrigues Type Formulas for Hypergeometric Difference Equations on Nonuniform Lattices

By building a second order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a generalized Rodrigues formula is also established.

math.CA↗