A <i>q</i>-Difference Equation and Fourier Series Expansions of <i>q</i>-Lidstone Polynomials

Abstract

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli polynomials generated by the third Jackson q-Bessel function, based on the Green’s function of a certain q-difference equation. Also, we provide the q-Fourier series expansions of these polynomials and derive some results related to them.

Keywords

• <i>q</i>-difference equation
• <i>q</i>-Lidstone polynomials
• Green functions
• <i>q</i>-Fourier series