Bessel Functions

We define the Bessel functions of the first kind as solutions of Bessel’s equation (Sect. 7.1). They can be expressed by means of the modified hypergeometric functions \({ }_{1}\mathcal {F}_{0}\) and \({ }_{1}\mathcal {F}_{1},\) as we will see. However, they have specific properties, which will be proved in Sect. 7.2. In Sect. 7.3, we introduce Bessel functions of the second kind, which allow to give the general solution of Bessel’s equation when its parameter is an integer.