DLMF: Notations G

Notations G

♦*♦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♦

$G_{n}$: Genocchi numbers; §24.15(i)
$\mathop{G\/}\nolimits\!\left(z\right)$: Barnes’ $G$ -function (or double gamma function); (5.17.1)
$\mathop{G\/}\nolimits\!\left(z\right)$: Goodwin–Staton integral; (7.2.12)
$\mathop{G\/}\nolimits\!\left(k\right)$: Waring’s function; §27.13(iii)
$\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$: auxiliary function for sine and cosine integrals; (6.2.18)
$\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$: auxiliary function for Fresnel integrals; (7.2.11)
$\mathop{g\/}\nolimits\!\left(k\right)$: Waring’s function; §27.13(iii)
$G_{s}(x)$: Bose–Einstein integral; (25.12.15)
$\mathop{G_{{p}}\/}\nolimits\!\left(z\right)$: product of gamma and incomplete gamma functions; §10.17(v)
$\mathop{G_{{p}}\/}\nolimits\!\left(z\right)$: product of gamma and incomplete gamma functions; §9.7(v)
$g_{{\mathit{e},m}}(h)$: joining factor for radial Mathieu functions; §28.22(i)
$g_{{\mathit{o},m}}(h)$: joining factor for radial Mathieu functions; §28.22(i)
$\mathop{G\/}\nolimits\!\left(n,\mathop{\chi\/}\nolimits\right)$: Gauss sum; (27.10.9)
$\mathop{G_{{\ell}}\/}\nolimits\!\left(\eta,\rho\right)$: irregular Coulomb radial function; (33.2.11)
$g(\epsilon,\ell;r)=\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$: notation used by Greene et al. (1979); ¶ ‣ §33.1
(with $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function)
$\mathop{G_{{n}}\/}\nolimits\!\left(p,q,x\right)$: shifted Jacobi polynomial; (18.1.2)
$\mathop{{G^{{m,n}}_{{p,q}}}\/}\nolimits\!\left(z;{a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}}\right)$: Meijer $G$ -function; (16.17.1)

$\mathop{{G^{{m,n}}_{{p,q}}}\/}\nolimits\!\left(z;\mathbf{a};\mathbf{b}\right)$: Meijer $G$ -function; (16.17.1)
$\EulerConstant$: Euler’s constant; (5.2.3)
$\mathop{\Gamma\/}\nolimits\!\left(z\right)$: gamma function; (5.2.1)
$\mathop{\Gamma _{{m}}\/}\nolimits\!\left(a\right)$: multivariate gamma function; §35.3(i)
$\mathop{\Gamma _{{q}}\/}\nolimits\!\left(z\right)$: $q$ -gamma function; (5.18.4)
$\mathop{\Gamma\/}\nolimits\!\left(a,z\right)$: incomplete gamma function; (8.2.2)
$\mathop{\gamma\/}\nolimits\!\left(a,z\right)$: incomplete gamma function; (8.2.1)
$\mathop{\gamma^{{*}}\/}\nolimits\!\left(a,z\right)$: incomplete gamma function; (8.2.6)
$\mathop{\mathrm{Gc}_{{m}}\/}\nolimits\!\left(z,h\right)$: Mathieu function; §28.26(i)
$\mathop{\mathrm{gd}\/}\nolimits x$: Gudermannian function; (4.23.39)
$\mathop{{\mathrm{gd}^{{-1}}}\/}\nolimits\!\left(x\right)$: inverse Gudermannian function; (4.23.41)
$\mathop{\mathrm{Ge}_{{n}}\/}\nolimits\!\left(z,q\right)$: modified Mathieu function; (28.20.7)
$\mathop{\mathrm{ge}_{{n}}\/}\nolimits\!\left(z,q\right)$: second solution, Mathieu’s equation; (28.5.2)
$\mathrm{Gey}_{n}(z,q)=\sqrt{\tfrac{1}{2}\pi}g_{{\mathit{o},n}}(h){\mathop{\mathrm{se}_{{n}}\/}\nolimits^{{\prime}}}\!\left(0,q\right)\mathop{{\mathrm{Ms}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z,h\right)$: notation used by Arscott (1964b), McLachlan (1947); ¶ ‣ §28.1
(with $\mathop{\mathrm{se}_{{n}}\/}\nolimits\!\left(z,q\right)$ : Mathieu function and $\mathop{{\mathrm{Ms}^{{(j)}}_{{n}}}\/}\nolimits\!\left(z,h\right)$ : radial Mathieu function)
$\mathop{\mathrm{Gi}\/}\nolimits\!\left(z\right)$: Scorer function (inhomogeneous Airy function); §9.12(i)
$\gradient$: gradient of differentiable scalar function; (1.6.20)
$\mathop{\mathrm{Gs}_{{m}}\/}\nolimits\!\left(z,h\right)$: Mathieu function; §28.26(i)