Odd and even $q$-type Lidstone polynomial sequences

TL;DR

This paper introduces two new classes of even and odd q-Lidstone polynomial sequences, exploring their fundamental properties such as generating functions, recurrence relations, and matrix representations.

Contribution

It presents the first comprehensive study of odd and even q-Lidstone polynomial sequences, including their properties and illustrative examples.

Findings

Established matrix and determinant representations

Derived generating functions and recurrence relations

Provided illustrative examples of the sequences

Abstract

In this paper, we introduce two types of general classes of even and odd $q$-Lidstone polynomial sequences. We prove essential properties related to them like the matrix and determinate form representation, the generating function, recurrence relation, and conjugate sequences. Some illustrative examples are included.