Notations H

$H_{\NVar{n}}$: harmonic number; (25.11.33)
$H\left(\NVar{s}\right)$: Euler sums; §25.16(ii)
$H\left(\NVar{x}\right)$: Heaviside function; (1.16.13)
$\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)$: Hermite polynomial; Table 18.3.1
$\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)$: Struve function; (11.2.1)
$h_{\NVar{n}}^{(1)}(\NVar{z})={\mathsf{h}^{(1)}_{n}}\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with ${\mathsf{h}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$ : spherical Bessel function of the third kind)
${\mathsf{h}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$: spherical Bessel function of the third kind; (10.47.5)
$h_{\NVar{n}}^{(2)}(\NVar{z})={\mathsf{h}^{(2)}_{n}}\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with ${\mathsf{h}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$ : spherical Bessel function of the third kind)
${\mathsf{h}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$: spherical Bessel function of the third kind; (10.47.6)
${H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)$: Bessel function of the third kind (or Hankel function); (10.2.5)
${H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)$: Bessel function of the third kind (or Hankel function); (10.2.6)
$H\left(\NVar{a},\NVar{u}\right)$: line-broadening function; (7.19.4)
$\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}\right)$: Hilbert transform; §1.14(v)
$H\left(\NVar{s},\NVar{z}\right)$: generalized Euler sums; §25.16(ii)
$\mathrm{H}(\NVar{z}|\NVar{\tau})=\theta_{1}\left(u\middle|\tau\right)$: Jacobi’s notation; §20.1
(with $\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)$ : theta function)
$\mathrm{H}_{1}(\NVar{z}|\NVar{\tau})=\theta_{2}\left(u\middle|\tau\right)$: Jacobi’s notation; §20.1
(with $\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)$ : theta function)
$\hat{H}_{\NVar{n}}\left(\NVar{x}\right)$: exceptional Hermite polynomial; §18.36(vi)

$H_{\NVar{n}}\left(\NVar{x}\,|\,\NVar{q}\right)$: continuous $q$ -Hermite polynomial; (18.28.16)
$h_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)$: discrete $q$ -Hermite I polynomial; (18.27.21)
$\tilde{h}_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)$: discrete $q$ -Hermite II polynomial; (18.27.23)
${H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho}\right)$: irregular Coulomb radial functions; (33.2.7)
$h\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)$: irregular Coulomb function; (33.14.7)
${{}_{\NVar{p}}H_{\NVar{q}}}\left({\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},% \dots,b_{q}}};\NVar{z}\right)$: bilateral hypergeometric function; (16.4.16)
$\mathit{hc}_{\NVar{p}}^{\NVar{m}}(\NVar{z},\NVar{\xi})$: paraboloidal wave function; §28.31(iii)
$(\NVar{s_{1}},\NVar{s_{2}})\mathit{Hf}_{\NVar{m}}\left(\NVar{a},\NVar{q_{m}};% \NVar{\alpha},\NVar{\beta},\NVar{\gamma},\NVar{\delta};\NVar{z}\right)$: Heun functions; §31.4
$(\NVar{s_{1}},\NVar{s_{2}})\mathit{Hf}_{\NVar{m}}^{\NVar{\nu}}\left(\NVar{a},% \NVar{q_{m}};\NVar{\alpha},\NVar{\beta},\NVar{\gamma},\NVar{\delta};\NVar{z}\right)$: path-multiplicative solutions of Heun’s equation; §31.6
$\mathit{Hh}_{\NVar{n}}\left(\NVar{z}\right)$: probability function; (7.18.12)
$\operatorname{Hi}\left(\NVar{z}\right)$: Scorer function (inhomogeneous Airy function); (9.12.5)
$\mathrm{Hi}_{\NVar{\nu}}(\NVar{z})={H^{(2)}_{\nu}}\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with ${H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)$ : Bessel function of the third kind (or Hankel function))
$\mathit{H\!\ell}\left(\NVar{a},\NVar{q};\NVar{\alpha},\NVar{\beta},\NVar{% \gamma},\NVar{\delta};\NVar{z}\right)$: Heun functions; (31.3.1)
$\mathit{Hp}_{\NVar{n},\NVar{m}}\left(\NVar{a},\NVar{q_{n,m}};\NVar{-n},\NVar{% \beta},\NVar{\gamma},\NVar{\delta};\NVar{z}\right)$: Heun polynomials; (31.5.2)
$\mathrm{Hs}_{\NVar{\nu}}(\NVar{z})={H^{(1)}_{\nu}}\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with ${H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)$ : Bessel function of the third kind (or Hankel function))
$\mathit{hs}_{\NVar{p}}^{\NVar{m}}(\NVar{z},\NVar{\xi})$: paraboloidal wave function; §28.31(iii)

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Notations H

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