17 - Bessel Functions

Abstract

This chapter focuses on the Bessel functions. The chapter reviews the different forms of Bessel's equation and the series expansions for Jυ(x) and Yυ(x). Various Bessel functions of fractional order are discussed. The chapter also discusses the asymptotic representations for Bessel functions for large arguments and for large orders. The zeros of Bessel functions and the different forms of Bessel's modified equation are reviewed. Series expansions for Iυ(x) and Kυ(x) and various modified Bessel functions of fractional order are discussed. The chapter also reviews the asymptotic representations of modified Bessel functions and the relationships between Bessel functions. Various definite integrals involving Bessel functions are discussed. The spherical Bessel functions including the differential equation, the spherical Bessel functions jn(x) and yn(x), the recurrence relations, and the series representations are also presented in the chapter.