Notations G

$G_{\NVar{n}}$: Genocchi numbers; §24.15(i)
$G\left(\NVar{k}\right)$: Waring’s function; §27.13(iii)
$g\left(\NVar{k}\right)$: Waring’s function; §27.13(iii)
$\mathrm{g}\left(\NVar{z}\right)$: auxiliary function for Fresnel integrals; (7.2.11)
$\mathrm{g}\left(\NVar{z}\right)$: auxiliary function for sine and cosine integrals; (6.2.18)
$G\left(\NVar{z}\right)$: Barnes’ $G$ -function (or double gamma function); (5.17.1)
$G\left(\NVar{z}\right)$: Goodwin–Staton integral; (7.2.12)
$g_{\mathit{e},\NVar{m}}(\NVar{h})$: joining factor for radial Mathieu functions; §28.22(i)
$g_{\mathit{o},\NVar{m}}(\NVar{h})$: joining factor for radial Mathieu functions; §28.22(i)
$G_{\NVar{p}}\left(\NVar{z}\right)$: rescaled terminant function; (9.7.22)
$G_{\NVar{s}}(\NVar{x})$: Bose–Einstein integral; (25.12.15)
$G\left(\NVar{n},\NVar{\chi}\right)$: Gauss sum; (27.10.9)
$\Gamma^{*}\left(\NVar{z}\right)$: scaled gamma function; (5.11.3)
$g_{\NVar{j}}$: Weierstrass lattice invariants $g_{2}$ , $g_{3}$ ; §23.3(i)
$G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}\right)$: irregular Coulomb radial function; (33.2.11)
$g(\NVar{\epsilon},\NVar{\ell};\NVar{r})=c\left(\epsilon,\ell;r\right)$: notation used by Greene et al. (1979); item Greene et al. (1979):
(with $c\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)$ : irregular Coulomb function)

$G_{\NVar{n}}\left(\NVar{p},\NVar{q},\NVar{x}\right)$: shifted Jacobi polynomial; (18.1.2)
${G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(\NVar{z};{\NVar{a_{1},\dots,a% _{p}}\atop\NVar{b_{1},\dots,b_{q}}}\right)$ or ${G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(\NVar{z};\NVar{\mathbf{a}};% \NVar{\mathbf{b}}\right)$: Meijer $G$ -function; (16.17.1)
$\gamma$: Euler’s constant; (5.2.3)
$\gamma_{\NVar{n}}$: Stieltjes constants; (25.2.5)
$\Gamma\left(\NVar{z}\right)$: gamma function; (5.2.1)
$\Gamma_{\NVar{m}}\left(\NVar{a}\right)$: multivariate gamma function; §35.3(i)
$\Gamma_{\NVar{q}}\left(\NVar{z}\right)$: $q$ -gamma function; (5.18.4)
$\Gamma\left(\NVar{a},\NVar{z}\right)$: incomplete gamma function; (8.2.2)
$\gamma^{*}\left(\NVar{a},\NVar{z}\right)$: incomplete gamma function; (8.2.6)
$\operatorname{gd}\NVar{x}$: Gudermannian function; (4.23.39)
${\operatorname{gd}^{-1}}\left(\NVar{x}\right)$: inverse Gudermannian function; (4.23.41)
$\operatorname{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$: modified Mathieu function; (28.20.7)
$\operatorname{ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$: second solution, Mathieu’s equation; (28.5.2)
$\mathrm{Gey}_{\NVar{n}}(\NVar{z},\NVar{q})=\sqrt{\tfrac{1}{2}\pi}g_{\mathit{o}% ,n}(h)\operatorname{se}_{n}'\left(0,q\right){\operatorname{Ms}^{(2)}_{n}}\left% (z,h\right)$: notation used by Arscott (1964b), McLachlan (1947); §28.1
(with $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter and ${\operatorname{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)$ : radial Mathieu function)
$\operatorname{Gi}\left(\NVar{z}\right)$: Scorer function (inhomogeneous Airy function); (9.12.4)
$\operatorname{grad}$: gradient of differentiable scalar function; (1.6.20)

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Notations G

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