Discrete Bessel functions and partial difference equations

Abstract

We introduce a new class of discrete Bessel functions and discrete modified Bessel functions of integer order. After obtaining some of their basic properties, we show that these functions lead to fundamental solutions of the discrete wave equation and discrete diffusion equation.

Keywords

• Bessel function
• modified Bessel function
• Bessel difference equation
• discrete wave equation
• discrete diffusion equation
• fundamental solution