§9.20 Software

ⓘ

Permalink:: http://dlmf.nist.gov/9.20
See also:: Annotations for Ch.9

§9.20(i) Introduction

ⓘ

Permalink:: http://dlmf.nist.gov/9.20.i
See also:: Annotations for §9.20 and Ch.9

In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. Citations in bulleted lists refer to papers for which research software has been made available and can be downloaded via the Web. References to research software that is available in other ways is listed separately.

A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C10d).

§9.20(ii) $\operatorname{Ai}\left(x\right)$ , $\operatorname{Ai}'\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $\operatorname{Bi}'\left(x\right)$ , $x\in\mathbb{R}$

ⓘ

Referenced by:: § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/9.20.ii
See also:: Annotations for §9.20 and Ch.9

•

Amos et al. (1977). Fortran.
•

Amos (1986). Fortran.
•

Fabijonas (2004). Fortran.
•

Prince (1975). Fortran.

§9.20(iii) $\operatorname{Ai}\left(z\right)$ , $\operatorname{Ai}'\left(z\right)$ , $\operatorname{Bi}\left(z\right)$ , $\operatorname{Bi}'\left(z\right)$ , $z\in\mathbb{C}$

ⓘ

Referenced by:: § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/9.20.iii
See also:: Annotations for §9.20 and Ch.9

•

Amos (1986). Fortran.
•

Fabijonas (2004). Fortran.
•

Gil et al. (2002a). Fortran.
•

Thompson and Barnett (1987). Fortran.

§9.20(iv) Real and Complex Zeros

ⓘ

Referenced by:: § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/9.20.iv
See also:: Annotations for §9.20 and Ch.9

•

Fabijonas (2004). Fortran.

§9.20(v) Integrals of $\operatorname{Ai}\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $x\in\mathbb{R}$

ⓘ

Referenced by:: § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/9.20.v
See also:: Annotations for §9.20 and Ch.9

•

MacLeod (1996a). Fortran.

§9.20(vi) Scorer Functions

ⓘ

Referenced by:: § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/9.20.vi
See also:: Annotations for §9.20 and Ch.9

•

MacLeod (1996a). Fortran.
•

Gil et al. (2002b). Fortran.

9.19 Approximations 10 Bessel Functions

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

§9.20 Software

Contents

§9.20(i) Introduction

§9.20(ii) $\operatorname{Ai}\left(x\right)$ , $\operatorname{Ai}'\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $\operatorname{Bi}'\left(x\right)$ , $x\in\mathbb{R}$

§9.20(iii) $\operatorname{Ai}\left(z\right)$ , $\operatorname{Ai}'\left(z\right)$ , $\operatorname{Bi}\left(z\right)$ , $\operatorname{Bi}'\left(z\right)$ , $z\in\mathbb{C}$

§9.20(iv) Real and Complex Zeros

§9.20(v) Integrals of $\operatorname{Ai}\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $x\in\mathbb{R}$

§9.20(vi) Scorer Functions

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

§9.20 Software

Contents

§9.20(i) Introduction

§9.20(ii) Ai⁡(x), Ai′⁡(x), Bi⁡(x), Bi′⁡(x), x∈ℝ

§9.20(iii) Ai⁡(z), Ai′⁡(z), Bi⁡(z), Bi′⁡(z), z∈ℂ

§9.20(iv) Real and Complex Zeros

§9.20(v) Integrals of Ai⁡(x), Bi⁡(x), x∈ℝ

§9.20(vi) Scorer Functions

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

§9.20(ii) $\operatorname{Ai}\left(x\right)$ , $\operatorname{Ai}'\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $\operatorname{Bi}'\left(x\right)$ , $x\in\mathbb{R}$

§9.20(iii) $\operatorname{Ai}\left(z\right)$ , $\operatorname{Ai}'\left(z\right)$ , $\operatorname{Bi}\left(z\right)$ , $\operatorname{Bi}'\left(z\right)$ , $z\in\mathbb{C}$

§9.20(v) Integrals of $\operatorname{Ai}\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $x\in\mathbb{R}$