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10 Bessel FunctionsComputation

§10.76 Approximations

Contents

§10.76(i) Introduction

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

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

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

Poquérusse and Alexiou (1999).

§10.76(iii) Other Functions

Bickley Functions

Blair et al. (1978).

Spherical Bessel Functions

Delic (1979b).

Kelvin Functions

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