Notations Notations G Notations I

Notations H

$H_n$

harmonic number; (25.11.33)

$H\left(s\right)$

Euler sums; §25.16(ii)

$H\left(x\right)$

Heaviside function; (1.16.13)

${\mathrm{𝐻𝑒}}_n\left(x\right)$

Hermite polynomial; Table 18.3.1

${𝐇}_{\nu }\left(z\right)$

Struve function; (11.2.1)

$h_n^{(1)}(z)={𝗁}_n^{(1)}\left(z\right)$

notation used by Abramowitz and Stegun (1964); §10.1
(with ${𝗁}_n^{(1)}\left(z\right)$: spherical Bessel function of the third kind)

${𝗁}_n^{(1)}\left(z\right)$

spherical Bessel function of the third kind; (10.47.5)

$h_n^{(2)}(z)={𝗁}_n^{(2)}\left(z\right)$

notation used by Abramowitz and Stegun (1964); §10.1
(with ${𝗁}_n^{(2)}\left(z\right)$: spherical Bessel function of the third kind)

${𝗁}_n^{(2)}\left(z\right)$

spherical Bessel function of the third kind; (10.47.6)

$H_{\nu }^{(1)}\left(z\right)$

Bessel function of the third kind (or Hankel function); (10.2.5)

$H_{\nu }^{(2)}\left(z\right)$

Bessel function of the third kind (or Hankel function); (10.2.6)

$H(a,u)$

line-broadening function; (7.19.4)

$\mathscr{H}\left(f\right)\left(x\right)$

Hilbert transform; §1.14(v)

$H(s,z)$

generalized Euler sums; §25.16(ii)

$\mathrm{H}(z|\tau )={\theta }_1\left(u\right|\tau )$

Jacobi’s notation; §20.1
(with ${\theta }_j\left(z\right|\tau )$: theta function)

${\mathrm{H}}_1(z|\tau )={\theta }_2\left(u\right|\tau )$

Jacobi’s notation; §20.1
(with ${\theta }_j\left(z\right|\tau )$: theta function)

${\widehat{H}}_n\left(x\right)$

exceptional Hermite polynomial; §18.36(vi)

$H_n\left(x|q\right)$

continuous $q$-Hermite polynomial; (18.28.16)

$h_n(x;q)$

discrete $q$-Hermite I polynomial; (18.27.21)

${\tilde{h}}_n(x;q)$

discrete $q$-Hermite II polynomial; (18.27.23)

$H_{\mathrm{\ell }}^{\pm }(\eta ,\rho )$

irregular Coulomb radial functions; (33.2.7)

$h(ϵ,\mathrm{\ell };r)$

irregular Coulomb function; (33.14.7)

${}_p{}^{}H_q^{}(\genfrac{}{}{0pt}{}{a_1,\mathrm{\dots },a_p}{b_1,\mathrm{\dots },b_q};z)$

bilateral hypergeometric function; (16.4.16)

${\mathrm{ℎ𝑐}}_p^m(z,\xi )$

paraboloidal wave function; §28.31(iii)

$(s_1,s_2){\mathrm{𝐻𝑓}}_m(a,q_m;\alpha ,\beta ,\gamma ,\delta ;z)$

Heun functions; §31.4

$(s_1,s_2){\mathrm{𝐻𝑓}}_m^{\nu }(a,q_m;\alpha ,\beta ,\gamma ,\delta ;z)$

path-multiplicative solutions of Heun’s equation; §31.6

${\mathrm{𝐻ℎ}}_n\left(z\right)$

probability function; (7.18.12)

$\mathrm{Hi}\left(z\right)$

Scorer function (inhomogeneous Airy function); (9.12.5)

${\mathrm{Hi}}_{\nu }(z)=H_{\nu }^{(2)}\left(z\right)$

notation used by Jeffreys and Jeffreys (1956); §10.1
(with $H_{\nu }^{(2)}\left(z\right)$: Bessel function of the third kind (or Hankel function))

$H\mathrm{\ell }(a,q;\alpha ,\beta ,\gamma ,\delta ;z)$

Heun functions; (31.3.1)

${\mathrm{𝐻𝑝}}_{n,m}(a,q_{n,m};-n,\beta ,\gamma ,\delta ;z)$

Heun polynomials; (31.5.2)

${\mathrm{Hs}}_{\nu }(z)=H_{\nu }^{(1)}\left(z\right)$

notation used by Jeffreys and Jeffreys (1956); §10.1
(with $H_{\nu }^{(1)}\left(z\right)$: Bessel function of the third kind (or Hankel function))

${\mathrm{ℎ𝑠}}_p^m(z,\xi )$

paraboloidal wave function; §28.31(iii)

Notations G Notations I

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