DLMF: Notations Q

Notations Q

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$\Rational$: set of all rational numbers; Common Notations and Definitions
$Q(z)=\tfrac{1}{2}\mathop{\mathrm{erfc}\/}\nolimits\!\left(z/\sqrt{2}\right)$: alternative notation for the complementary error function; §7.1
(with $\mathop{\mathrm{erfc}\/}\nolimits z$ : complementary error function)
$Q_{z}(a)=\mathop{\Gamma\/}\nolimits\!\left(a,z\right)$: notation used by Batchelder (1967, p. 63); §8.1
(with $\mathop{\Gamma\/}\nolimits\!\left(a,z\right)$ : incomplete gamma function)
$\mathop{\mathsf{Q}_{{\nu}}\/}\nolimits\!\left(x\right)$ : $\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$ with $\mu=0$: ; ¶ ‣ §14.3(i)
$\mathop{\mathsf{Q}_{{\nu}}\/}\nolimits\!\left(x\right)$ : $\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$ with $\mu=0$: ; §14.1
$\mathop{Q_{{n}}\/}\nolimits\!\left(x;\alpha,\beta,N\right)$: Hahn polynomial; Table 18.19.1
$\mathop{Q_{{\nu}}\/}\nolimits\!\left(z\right)$ : $\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$ with $\mu=0$: ; §14.21(i)
$\mathop{Q_{{\nu}}\/}\nolimits\!\left(z\right)$ : $\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$ with $\mu=0$: ; ¶ ‣ §14.3(ii)
$\mathop{Q_{{\nu}}\/}\nolimits\!\left(z\right)$ : $\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$ with $\mu=0$: ; §14.1
$\mathrm{Q}_{\nu}^{\mu}(x)=\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$: notation used by Erdélyi et al. (1953a), Olver (1997b); §14.1
(with $\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Ferrers function of the second kind)
$\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$: Ferrers function of the second kind; (14.3.2)
$\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$: associated Legendre function of the second kind; (14.3.7)
$\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$: associated Legendre function of the second kind; §14.21(i)
$Q_{{\nu}}^{{\mu}}(x)=\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$: notation used by Magnus et al. (1966); §14.1
(with $\mathop{\mathsf{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Ferrers function of the second kind)

$\mathfrak{Q}_{{\nu}}^{{\mu}}(z)=\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$: notation used by Magnus et al. (1966); §14.1
(with $\mathop{Q^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$ : associated Legendre function of the second kind)
$\mathop{\boldsymbol{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$: Olver’s associated Legendre function; §14.21(i)
$\mathop{\boldsymbol{Q}^{{\mu}}_{{\nu}}\/}\nolimits\!\left(z\right)$: Olver’s associated Legendre function; (14.3.10)
$\mathop{\widehat{\mathsf{Q}}^{{-\mu}}_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right)$: conical function; (14.20.2)
$\mathop{Q\/}\nolimits\!\left(a,z\right)$: normalized incomplete gamma function; (8.2.4)
$Q_{\ell}(\epsilon,r)=-(2\ell+1)!\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)/(2^{{\ell+1}}A(\epsilon,\ell))$: notation used by Curtis (1964a); ¶ ‣ §33.1
(with $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function and $!$ : $n!$ : factorial)
$\mathop{Q_{{n}}\/}\nolimits\!\left(x;a,b\,|\, q\right)$: Al-Salam–Chihara polynomial; (18.28.7)
$\mathop{Q_{{n}}\/}\nolimits\!\left(x;a,b\,|\, q^{{-1}}\right)$: $q^{{-1}}$ -Al-Salam–Chihara polynomial; (18.28.9)
$\mathop{Q_{{n}}\/}\nolimits\!\left(x;\alpha,\beta,N;q\right)$: $q$ -Hahn polynomial; (18.27.3)
$\mathop{\mathit{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(z,\gamma^{2}\right)$: spheroidal wave function of complex argument; §30.6
$\mathrm{Qs}^{{m}}_{{n}}(z,\gamma^{2})=\mathop{\mathit{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(z,\gamma^{2}\right)$: notation used by Meixner and Schäfke (1954) for the spheroidal wave function of complex argument; §30.1
(with $\mathop{\mathit{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(z,\gamma^{2}\right)$ : spheroidal wave function of complex argument)
$\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$: spheroidal wave function of the second kind; §30.5
$\mathrm{qs}^{{m}}_{{n}}(x,\gamma^{2})=\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$: notation used by Meixner and Schäfke (1954) for the spheroidal wave function of the second kind; §30.1
(with $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind)