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DLMF: §10.76 Approximations ‣ Computation ‣ Chapter 10 Bessel Functions
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10 Bessel FunctionsComputation

§10.76 Approximations

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Keywords:
Bessel functions, approximations
Permalink:
http://dlmf.nist.gov/10.76
See also:
Annotations for Ch.10
Contents
  1. §10.76(i) Introduction
  2. §10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
  3. §10.76(iii) Other Functions

§10.76(i) Introduction

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Permalink:
http://dlmf.nist.gov/10.76.i
See also:
Annotations for §10.76 and Ch.10

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

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See also:
Annotations for §10.76(ii), §10.76 and Ch.10

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

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See also:
Annotations for §10.76(ii), §10.76 and Ch.10

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

Complex Variable; Real Order

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See also:
Annotations for §10.76(ii), §10.76 and Ch.10

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

Real Variable; Imaginary Order

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Keywords:
approximations, modified Bessel functions, of imaginary order
See also:
Annotations for §10.76(ii), §10.76 and Ch.10

Poquérusse and Alexiou (1999).

§10.76(iii) Other Functions

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Permalink:
http://dlmf.nist.gov/10.76.iii
See also:
Annotations for §10.76 and Ch.10

Bickley Functions

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Keywords:
Bickley function, approximations
See also:
Annotations for §10.76(iii), §10.76 and Ch.10

Blair et al. (1978).

Spherical Bessel Functions

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Keywords:
approximations, spherical Bessel functions
See also:
Annotations for §10.76(iii), §10.76 and Ch.10

Delic (1979b).

Kelvin Functions

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Keywords:
Kelvin functions, approximations
See also:
Annotations for §10.76(iii), §10.76 and Ch.10

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

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