§9.1 Special Notation

ⓘ

Keywords:: Airy functions, Scorer functions, generalized, inhomogeneous Airy functions, notation
Permalink:: http://dlmf.nist.gov/9.1
See also:: Annotations for Ch.9

(For other notation see Notation for the Special Functions.)

$k$	nonnegative integer, except in §9.9(iii).
$x$	real variable.
$z(=x+\mathrm{i}y)$	complex variable.
$\delta$	arbitrary small positive constant.
primes	derivatives with respect to argument.

The main functions treated in this chapter are the Airy functions $\operatorname{Ai}\left(z\right)$ and $\operatorname{Bi}\left(z\right)$ , and the Scorer functions $\operatorname{Gi}(z)$ and $\operatorname{Hi}(z)$ (also known as inhomogeneous Airy functions).

Other notations that have been used are as follows: $\operatorname{Ai}\left(-x\right)$ and $\operatorname{Bi}\left(-x\right)$ for $\operatorname{Ai}\left(x\right)$ and $\operatorname{Bi}\left(x\right)$ (Jeffreys (1928), later changed to $\operatorname{Ai}\left(x\right)$ and $\operatorname{Bi}\left(x\right)$ ); $U(x)=\sqrt{\pi}\operatorname{Bi}\left(x\right)$ , $V(x)=\sqrt{\pi}\operatorname{Ai}\left(x\right)$ (Fock (1945)); $A(x)=3^{-\ifrac{1}{3}}\pi\operatorname{Ai}\left(-3^{-\ifrac{1}{3}}x\right)$ (Szegő (1967, §1.81)); $e_{0}(x)=\pi\operatorname{Hi}(-x)$ , $\widetilde{e}_{0}(x)=-\pi\operatorname{Gi}(-x)$ (Tumarkin (1959)).

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.

§9.1 Special Notation

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