About the Project
Notations

Notations H

H n
harmonic number; (25.11.33)
H ( s )
Euler sums; §25.16(ii)
H ( x )
Heaviside function; (1.16.13)
𝐻𝑒 n ( x )
Hermite polynomial; Table 18.3.1
𝐇 ν ( z )
Struve function; (11.2.1)
h n ( 1 ) ( z ) = 𝗁 n ( 1 ) ( z )
notation used by Abramowitz and Stegun (1964); §10.1
(with 𝗁n(1)(z): spherical Bessel function of the third kind)
𝗁 n ( 1 ) ( z )
spherical Bessel function of the third kind; (10.47.5)
h n ( 2 ) ( z ) = 𝗁 n ( 2 ) ( z )
notation used by Abramowitz and Stegun (1964); §10.1
(with 𝗁n(2)(z): spherical Bessel function of the third kind)
𝗁 n ( 2 ) ( z )
spherical Bessel function of the third kind; (10.47.6)
H ν ( 1 ) ( z )
Bessel function of the third kind (or Hankel function); (10.2.5)
H ν ( 2 ) ( z )
Bessel function of the third kind (or Hankel function); (10.2.6)
H ( a , u )
line-broadening function; (7.19.4)
( f ) ( x )
Hilbert transform; §1.14(v)
H ( s , z )
generalized Euler sums; §25.16(ii)
H ( z | τ ) = θ 1 ( u | τ )
Jacobi’s notation; §20.1
(with θj(z|τ): theta function)
H 1 ( z | τ ) = θ 2 ( u | τ )
Jacobi’s notation; §20.1
(with θj(z|τ): theta function)
H ^ n ( x )
exceptional Hermite polynomial; §18.36(vi)
H n ( x | q )
continuous q-Hermite polynomial; (18.28.16)
h n ( x ; q )
discrete q-Hermite I polynomial; (18.27.21)
h ~ n ( x ; q )
discrete q-Hermite II polynomial; (18.27.23)
H ± ( η , ρ )
irregular Coulomb radial functions; (33.2.7)
h ( ϵ , ; r )
irregular Coulomb function; (33.14.7)
H q p ( a 1 , , a p b 1 , , b q ; z )
bilateral hypergeometric function; (16.4.16)
ℎ𝑐 p m ( z , ξ )
paraboloidal wave function; §28.31(iii)
( s 1 , s 2 ) 𝐻𝑓 m ( a , q m ; α , β , γ , δ ; z )
Heun functions; §31.4
( s 1 , s 2 ) 𝐻𝑓 m ν ( a , q m ; α , β , γ , δ ; z )
path-multiplicative solutions of Heun’s equation; §31.6
𝐻ℎ n ( z )
probability function; (7.18.12)
Hi ( z )
Scorer function (inhomogeneous Airy function); (9.12.5)
Hi ν ( z ) = H ν ( 2 ) ( z )
notation used by Jeffreys and Jeffreys (1956); §10.1
(with Hν(2)(z): Bessel function of the third kind (or Hankel function))
H ( a , q ; α , β , γ , δ ; z )
Heun functions; (31.3.1)
𝐻𝑝 n , m ( a , q n , m ; n , β , γ , δ ; z )
Heun polynomials; (31.5.2)
Hs ν ( z ) = H ν ( 1 ) ( z )
notation used by Jeffreys and Jeffreys (1956); §10.1
(with Hν(1)(z): Bessel function of the third kind (or Hankel function))
ℎ𝑠 p m ( z , ξ )
paraboloidal wave function; §28.31(iii)