# Notations Q

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