§10.76 Approximations

Keywords:: Bessel functions
Permalink:: http://dlmf.nist.gov/10.76

Contents

§10.76(i) Introduction
§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
§10.76(iii) Other Functions

§10.76(i) Introduction

Permalink:: http://dlmf.nist.gov/10.76.i

Because of the comprehensive nature of more recent software packages (§10.77), the following subsections include only references that give representative examples of the kind of approximations that can be used to generate the functions that appear in the present chapter. For references to other approximations, see for example, Luke (1975, §9.13.3).

§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions

Keywords:: Bessel functions, Hankel functions, integrals, modified Bessel functions
Permalink:: http://dlmf.nist.gov/10.76.ii

¶ Real Variable and Order $:$ Functions

Luke (1971b, a, 1972), Luke (1975, Tables 9.1, 9.2, 9.5, 9.6, 9.11–9.15, 9.17–9.21), Weniger and Čížek (1990), Németh (1992, Chapters 4–6).

¶ Real Variable and Order $:$ Zeros

Keywords:: zeros of Bessel functions (including derivatives)

Piessens (1984a, 1990), Piessens and Ahmed (1986), Németh (1992, Chapter 7).

¶ Real Variable and Order $:$ Integrals

Luke (1975, Tables 9.3, 9.4, 9.7–9.9, 9.16, 9.22), Németh (1992, Chapter 10).

¶ Complex Variable; Real Order

Luke (1975, Tables 9.23–9.28), Coleman and Monaghan (1983), Coleman (1987), Zhang (1996), Zhang and Belward (1997).

¶ Real Variable; Imaginary Order

Keywords:: modified Bessel functions

Poquérusse and Alexiou (1999).

§10.76(iii) Other Functions

Permalink:: http://dlmf.nist.gov/10.76.iii

¶ Bickley Functions

Keywords:: Bickley function

Blair et al. (1978).

¶ Spherical Bessel Functions

Keywords:: spherical Bessel functions

Delic (1979b).

¶ Kelvin Functions

Keywords:: Kelvin functions

Luke (1975, Table 9.10), Németh (1992, Chapter 9).