Generalized Bessel Functions of the First Kind

Abstract

We begin with a brief outline of Bessel functions, which will be needed in the next chapters. We recall here the Bessel, modified Bessel, spherical Bessel and modified spherical Bessel functions and define the generalized Bessel function. Some general properties of generalized Bessel functions are discussed in this chapter. These include: recursive formulas, differentiation formula, integral representations. We recall here also the Gaussian hypergeometric function with its basic properties which will have applications in Chap. 3. Finally, at the end of this chapter we list some classical inequalities which will be used in the sequel.