CHAPTER 17 - Bessel Functions

Abstract

This chapter discusses the different aspects of Bessel function. In standard form, Bessel's equation is either written as x2d2y/ dx2 + x dy/dx + (x2–ν2)y = 0 where the real parameter ν determines the nature of the two linearly independent solutions of the equation. By convention, ν is understood to be any real number that is not an integer, and when integral values of this parameter are involved ν is replaced by n. A second solution of Bessel's equation that is always linearly independent of Yν(x) is Yν(x), irrespective of the value of ν. The Bessel functions of fractional order are also discussed in the chapter.