DLMF: Notations A

Notations A

♦*♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

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

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