Recurrence Relations of the Hypergeometric-type functions on the quadratic-type lattices

TL;DR

This paper develops a systematic method to derive recurrence relations for hypergeometric-type functions on quadratic lattices, with applications to related polynomials, enhancing understanding of their structural properties.

Contribution

It introduces a new systematic approach for constructing recurrence relations for hypergeometric-type solutions on quadratic lattices, expanding the theoretical framework.

Findings

Derived new recurrence relations for hypergeometric-type functions

Applied relations to polynomial solutions on quadratic lattices

Enhanced understanding of solution structures on quadratic lattices

Abstract

The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We introduce some recurrence relations for such solutions by also considering their applications to polynomials on the quadratic-type lattices.