DLMF: Notations H

Notations H

♦*♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

$\mathop{H\/}\nolimits\!\left(s\right)$: Euler sums; §25.16(ii)
$\mathop{H\/}\nolimits\!\left(x\right)$: Heaviside function; (1.16.13)
$\mathop{H_{{n}}\/}\nolimits\!\left(x\right)$: Hermite polynomial; Table 18.3.1
$\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$: Struve function; (11.2.1)
$\mathop{\mathit{He}_{{n}}\/}\nolimits\!\left(x\right)$: Hermite polynomial; Table 18.3.1
$\mathop{{H^{{(1)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$: Bessel function of the third kind (or Hankel function); (10.2.5)
$\mathop{{H^{{(2)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$: Bessel function of the third kind (or Hankel function); (10.2.6)
$h_{n}^{{(1)}}(z)=\mathop{{\mathsf{h}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with $\mathop{{\mathsf{h}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the third kind)
$\mathop{{\mathsf{h}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$: spherical Bessel function of the third kind; (10.47.5)
$h_{n}^{{(2)}}(z)=\mathop{{\mathsf{h}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with $\mathop{{\mathsf{h}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the third kind)
$\mathop{{\mathsf{h}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$: spherical Bessel function of the third kind; (10.47.6)
$\mathop{H\/}\nolimits\!\left(s,z\right)$: generalized Euler sums; §25.16(ii)
$\mathop{\mathcal{H}\/}\nolimits\left(f;x\right)$: Hilbert transform; §1.14(v)
$\mathrm{H}(z|\tau)=\mathop{\theta _{{1}}\/}\nolimits\!\left(u\middle|\tau\right)$: Jacobi’s notation; ¶ ‣ §20.1
(with $\mathop{\theta _{{j}}\/}\nolimits\!\left(z\middle|\tau\right)$ : theta function)
$\mathop{H\/}\nolimits\!\left(a,u\right)$: line-broadening function; (7.19.4)
$\mathop{H_{{n}}\/}\nolimits\!\left(x\,|\, q\right)$: continuous $q$ -Hermite polynomial; (18.28.16)
$\mathop{h_{{n}}\/}\nolimits\!\left(x\,|\, q\right)$: continuous $q^{{-1}}$ -Hermite polynomial; (18.28.18)

$\mathrm{H}_{1}(z|\tau)=\mathop{\theta _{{2}}\/}\nolimits\!\left(u\middle|\tau\right)$: Jacobi’s notation; ¶ ‣ §20.1
(with $\mathop{\theta _{{j}}\/}\nolimits\!\left(z\middle|\tau\right)$ : theta function)
$\mathop{h_{{n}}\/}\nolimits\!\left(x;q\right)$: discrete $q$ -Hermite I polynomial; (18.27.21)
$\mathop{\tilde{h}_{{n}}\/}\nolimits\!\left(x;q\right)$: discrete $q$ -Hermite II polynomial; (18.27.23)
$\mathop{{H^{{\pm}}_{{\ell}}}\/}\nolimits\!\left(\eta,\rho\right)$: irregular Coulomb radial functions; (33.2.7)
$\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$: irregular Coulomb function; (33.14.7)
$\mathop{{{}_{{p}}H_{{q}}}\/}\nolimits\!\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right)$: bilateral hypergeometric function; (16.4.16)
$\mathit{hc}_{p}^{m}(z,\xi)$: paraboloidal wave function; §28.31(iii)
$\mathop{(s_{1},s_{2})\mathit{Hf}_{{m}}\/}\nolimits\!\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$: Heun functions; §31.4
$\mathop{(s_{1},s_{2})\mathit{Hf}_{{m}}^{{\nu}}\/}\nolimits\!\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$: path-multiplicative solutions of Heun’s equation; §31.6
$\mathop{\mathit{Hh}_{{n}}\/}\nolimits\!\left(z\right)$: probability function; (7.18.12)
$\mathop{\mathit{Hh}_{{n}}\/}\nolimits\!\left(z\right)$: probability function; §12.7(ii)
$\mathop{\mathrm{Hi}\/}\nolimits\!\left(z\right)$: Scorer function (inhomogeneous Airy function); §9.12(i)
$\mathrm{Hi}_{\nu}(z)=\mathop{{H^{{(2)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with $\mathop{{H^{{(2)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$ : Bessel function of the third kind (or Hankel function))
$\mathop{\mathit{H\!\ell}\/}\nolimits\!\left(a,q;\alpha,\beta,\gamma,\delta;z\right)$: Heun functions; (31.3.1)
$\mathop{\mathit{Hp}_{{n,m}}\/}\nolimits\!\left(a,q_{{n,m}};-n,\beta,\gamma,\delta;z\right)$: Heun polynomials; (31.5.2)
$\mathrm{Hs}_{\nu}(z)=\mathop{{H^{{(1)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with $\mathop{{H^{{(1)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$ : Bessel function of the third kind (or Hankel function))
$\mathit{hs}_{p}^{m}(z,\xi)$: paraboloidal wave function; §28.31(iii)