Microfluidics: Modeling, Mechanics and Mathematics

4.4 Fourier-Bessel Series

4.4.1 Introduction

In section 4.3, we learned that any function can be represented by a Fourier series. A Fourier series is nothing other than an infinite series of sine and cosine terms that have to be added in order to approximate the desired function. Sine and cosine functions are not the only functions that can be used for such a series expansion. In fact, a function can be represented as any linear combination of orthogonal functions. Sine and cosine functions qualify as such, but many more functions can be used.

One particularly useful class of functions are Bessel functions (see section 3.2.4). The most important one of this set of functions is the Bessel function of first kind J_ν of order ν. The Bessel functions ...