Notations A

$\forall$: for every; Common Notations and Definitions
$A$: Glaisher’s constant; (5.17.6)
$a_{\NVar{k}}$: $k$ th zero of Airy $\operatorname{Ai}$ ; §9.9(i)
$a^{\prime}_{\NVar{k}}$: $k$ th zero of Airy $\operatorname{Ai}'$ ; §9.9(i)
$A(\NVar{x})=3^{-\ifrac{1}{3}}\pi\operatorname{Ai}\left(-3^{-\ifrac{1}{3}}x\right)$: notation used by Szegő (1967); §9.1
(with $\operatorname{Ai}\left(\NVar{z}\right)$ : Airy function and $\pi$ : the ratio of the circumference of a circle to its diameter)
$A_{\NVar{m},\NVar{s}}\left(\NVar{q}\right)$: $q$ -Euler number; (17.3.8)
$a_{\NVar{m},\NVar{s}}\left(\NVar{q}\right)$: $q$ -Stirling number; (17.3.9)
$a_{\NVar{n}}\left(\NVar{q}\right)$: eigenvalues of Mathieu equation; §28.2(v)
$A_{\NVar{n}}\left(\NVar{z}\right)$: generalized Airy function; §9.13(i)
$A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$: Bessel function of matrix argument (first kind); §35.5(i)
$\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)$: Anger–Weber function; (11.10.4)
$a^{\NVar{n}}_{\NVar{\nu}}\left(\NVar{k^{2}}\right)$: eigenvalues of Lamé’s equation; §29.3(i)
$A_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)$: generalized Airy function; §9.13(ii)
$\operatorname{Ai}\left(\NVar{z}\right)$: Airy function; §9.2(i)
$\alpha$: fine structure constant; §18.39(ii)
$\operatorname{am}\left(\NVar{x},\NVar{k}\right)$: Jacobi’s amplitude function; (22.16.1)
$\operatorname{arccd}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arccn}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{Arccos}\NVar{z}$: general arccosine function; (4.23.2)
$\operatorname{arccos}\NVar{z}$: arccosine function; §4.23(ii)
$\operatorname{Arccosh}\NVar{z}$: general inverse hyperbolic cosine function; (4.37.2)
$\operatorname{arccosh}\NVar{z}$: inverse hyperbolic cosine function; §4.37(ii)
$\operatorname{Arccot}\NVar{z}$: general arccotangent function; (4.23.6)
$\operatorname{arccot}\NVar{z}$: arccotangent function; (4.23.9)
$\operatorname{Arccoth}\NVar{z}$: general inverse hyperbolic cotangent function; (4.37.6)
$\operatorname{arccoth}\NVar{z}$: inverse hyperbolic cotangent function; (4.37.9)

$\operatorname{arccs}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{Arccsc}\NVar{z}$: general arccosecant function; (4.23.4)
$\operatorname{arccsc}\NVar{z}$: arccosecant function; (4.23.7)
$\operatorname{Arccsch}\NVar{z}$: general inverse hyperbolic cosecant function; (4.37.4)
$\operatorname{arccsch}\NVar{z}$: inverse hyperbolic cosecant function; (4.37.7)
$\operatorname{arcdc}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcdn}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcds}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcnc}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcnd}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcns}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcsc}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{arcsd}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{Arcsec}\NVar{z}$: general arcsecant function; (4.23.5)
$\operatorname{arcsec}\NVar{z}$: arcsecant function; (4.23.8)
$\operatorname{Arcsech}\NVar{z}$: general inverse hyperbolic secant function; (4.37.5)
$\operatorname{arcsech}\NVar{z}$: inverse hyperbolic secant function; (4.37.8)
$\operatorname{Arcsin}\NVar{z}$: general arcsine function; (4.23.1)
$\operatorname{arcsin}\NVar{z}$: arcsine function; §4.23(ii)
$\operatorname{Arcsinh}\NVar{z}$: general inverse hyperbolic sine function; (4.37.1)
$\operatorname{arcsinh}\NVar{z}$: inverse hyperbolic sine function; §4.37(ii)
$\operatorname{arcsn}\left(\NVar{x},\NVar{k}\right)$: inverse Jacobian elliptic function; §22.15(i)
$\operatorname{Arctan}\NVar{z}$: general arctangent function; (4.23.3)
$\operatorname{arctan}\NVar{z}$: arctangent function; §4.23(ii)
$\operatorname{Arctanh}\NVar{z}$: general inverse hyperbolic tangent function; (4.37.3)
$\operatorname{arctanh}\NVar{z}$: inverse hyperbolic tangent function; §4.37(ii)

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