§ 9.1. Special Notation

Permalink:: http://dlmf.nist.gov/9.1

(For other notation see LABEL:about.notations.)

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

Defines:: $k$ : nonnegative integer, $x$ : real variable, $z$ : complex variable and $\delta$ : small positive constant
Permalink:: http://dlmf.nist.gov/9.1.T1

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

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