Notations Notations P Notations R

Notations Q

$\mathbb{Q}$

set of all rational numbers; Common Notations and Definitions

$Q(z)=\frac{1}{2}\mathrm{erfc}\left(z/\sqrt{2}\right)$

alternative notation for the complementary error function; §7.1
(with $\mathrm{erfc}z$: complementary error function)

${𝖰}_{\nu }\left(x\right)={𝖰}_{\nu }^0\left(x\right)$

Ferrers function of the second kind; §14.2(ii)
(with ${𝖰}_{\nu }^{\mu }\left(x\right)$: Ferrers function of the second kind)

${𝑸}_{\nu }\left(z\right)={𝑸}_{\nu }^0\left(z\right)$

Olver’s associated Legendre function; §14.2(ii)
(with ${𝑸}_{\nu }^{\mu }\left(z\right)$: Olver’s associated Legendre function)

$Q_z(a)=\mathrm{\Gamma }(a,z)$

notation used by Batchelder (1967, p. 63); §8.1
(with $\mathrm{\Gamma }(a,z)$: incomplete gamma function)

${\widehat{𝖰}}_{-\frac{1}{2}+\mathrm{i}\tau }^{-\mu }\left(x\right)$

conical function; (14.20.2)

${\mathrm{Q}}_{\nu }^{\mu }(x)={𝖰}_{\nu }^{\mu }\left(x\right)$

notation used by Erdélyi et al. (1953a), Olver (1997b); §14.1
(with ${𝖰}_{\nu }^{\mu }\left(x\right)$: Ferrers function of the second kind)

${𝖰}_{\nu }^{\mu }\left(x\right)$

Ferrers function of the second kind; (14.3.2)

$Q_{\nu }^{\mu }(x)={𝖰}_{\nu }^{\mu }\left(x\right)$

notation used by Magnus et al. (1966); §14.1
(with ${𝖰}_{\nu }^{\mu }\left(x\right)$: Ferrers function of the second kind)

$Q_{\nu }^{\mu }\left(z\right)$

associated Legendre function of the second kind; §14.21(i)

${𝔔}_{\nu }^{\mu }(z)=Q_{\nu }^{\mu }\left(z\right)$

notation used by Magnus et al. (1966); §14.1
(with $Q_{\nu }^{\mu }\left(z\right)$: associated Legendre function of the second kind)

${𝑸}_{\nu }^{\mu }\left(z\right)$

Olver’s associated Legendre function; §14.21(i)

$Q(a,z)$

normalized incomplete gamma function; (8.2.4)

$Q_{\mathrm{\ell }}(ϵ,r)=-(2\mathrm{\ell }+1)!h(ϵ,\mathrm{\ell };r)/(2^{\mathrm{\ell }+1}A(ϵ,\mathrm{\ell }))$

notation used by Curtis (1964a); item Curtis (1964a):
(with $h(ϵ,\mathrm{\ell };r)$: irregular Coulomb function and $!$: factorial (as in $n!$))

$Q_n^{(\lambda )}(x;a,b,c)$

Pollaczek polynomial; (18.35.2_2)

$Q_n(x;a,b|q^{-1})$

$q^{-1}$-Al-Salam–Chihara polynomial; (18.28.9)

$Q_n(x;\alpha ,\beta ,N)$

Hahn polynomial; Table 18.19.1

$Q_n(x;\alpha ,\beta ,N;q)$

$q$-Hahn polynomial; (18.27.3)

${\mathrm{qs}}_n^m(x,{\gamma }^2)={\mathrm{𝖰𝗌}}_n^m(x,{\gamma }^2)$

notation used by Meixner and Schäfke (1954) for the spheroidal wave function of the second kind; §30.1
(with ${\mathrm{𝖰𝗌}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind)

${\mathrm{𝖰𝗌}}_n^m(x,{\gamma }^2)$

spheroidal wave function of the second kind; §30.5

${\mathrm{Qs}}_n^m(z,{\gamma }^2)={\mathrm{𝑄𝑠}}_n^m(z,{\gamma }^2)$

notation used by Meixner and Schäfke (1954) for the spheroidal wave function of complex argument; §30.1
(with ${\mathrm{𝑄𝑠}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument)

${\mathrm{𝑄𝑠}}_n^m(z,{\gamma }^2)$

spheroidal wave function of complex argument; §30.6

Notations P Notations R

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