# Notations Q

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$\mathbb{Q}$
set of all rational numbers; Common Notations and Definitions
$Q(\NVar{z})=\tfrac{1}{2}\operatorname{erfc}\left(z/\sqrt{2}\right)$
alternative notation for the complementary error function; §7.1
$\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{Q}^{0}_{\nu}\left(x\right)$
Ferrers function of the second kind; §14.2(ii)
$Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}\left(z\right)$
Legendre function of the second kind; §14.2(ii)
$Q_{\NVar{z}}(\NVar{a})=\Gamma\left(a,z\right)$
notation used by Batchelder (1967, p. 63); §8.1
$\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1}{2}+i\tau}}\left(\NVar{x}\right)$
conical function; (14.20.2)
$\mathrm{Q}_{\NVar{\nu}}^{\NVar{\mu}}(\NVar{x})=\mathsf{Q}^{\mu}_{\nu}\left(x\right)$
notation used by Erdélyi et al. (1953a), Olver (1997b); §14.1
$\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)$
Ferrers function of the second kind; (14.3.2)
$Q_{\NVar{\nu}}^{\NVar{\mu}}(\NVar{x})=\mathsf{Q}^{\mu}_{\nu}\left(x\right)$
notation used by Magnus et al. (1966); §14.1
$Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)$
associated Legendre function of the second kind; §14.21(i)
$\mathfrak{Q}_{\NVar{\nu}}^{\NVar{\mu}}(\NVar{z})=Q^{\mu}_{\nu}\left(z\right)$
notation used by Magnus et al. (1966); §14.1
$\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)$
Olver’s associated Legendre function; §14.21(i)
$Q\left(\NVar{a},\NVar{z}\right)$
normalized incomplete gamma function; (8.2.4)
$Q_{\NVar{\ell}}(\NVar{\epsilon},\NVar{r})=-(2\ell+1)!h\left(\epsilon,\ell;r% \right)/(2^{\ell+1}A(\epsilon,\ell))$
notation used by Curtis (1964a); item Curtis (1964a):
$Q_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b}\,|\,\NVar{q}^{-1}\right)$
$q^{-1}$-Al-Salam–Chihara polynomial; (18.28.9)
$Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{N}\right)$
Hahn polynomial; Table 18.19.1
$Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{N};\NVar{q}\right)$
$q$-Hahn polynomial; (18.27.3)
$\mathrm{qs}^{\NVar{m}}_{\NVar{n}}(\NVar{x},\NVar{\gamma^{2}})=\mathsf{Qs}^{m}_% {n}\left(x,\gamma^{2}\right)$
notation used by Meixner and Schäfke (1954) for the spheroidal wave function of the second kind; §30.1
$\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$
spheroidal wave function of the second kind; §30.5
$\mathrm{Qs}^{\NVar{m}}_{\NVar{n}}(\NVar{z},\NVar{\gamma^{2}})=\mathit{Qs}^{m}_% {n}\left(z,\gamma^{2}\right)$
notation used by Meixner and Schäfke (1954) for the spheroidal wave function of complex argument; §30.1
$\mathit{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma^{2}}\right)$
spheroidal wave function of complex argument; §30.6