Digital Library of Mathematical Functions
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Notations

Notations H

*ABCDEFG♦H♦IJKLMNOPQRSTUVWXYZ
H(s)
Euler sums; 25.16(ii)
H(x)
Heaviside function; (1.16.13)
Hn(x)
Hermite polynomial; 18.3.1
Hν(z)
Struve function; (11.2.1)
Hen(x)
Hermite polynomial; 18.3.1
Hν(1)(z)
Bessel function of the third kind (or Hankel function); (10.2.5)
Hν(2)(z)
Bessel function of the third kind (or Hankel function); (10.2.6)
hn(1)(z)=hn(1)(z)
notation used by Abramowitz and Stegun (1964); 10.1
(with hn(1)(z): spherical Bessel function of the third kind)
hn(1)(z)
spherical Bessel function of the third kind; (10.47.5)
hn(2)(z)=hn(2)(z)
notation used by Abramowitz and Stegun (1964); 10.1
(with hn(2)(z): spherical Bessel function of the third kind)
hn(2)(z)
spherical Bessel function of the third kind; (10.47.6)
H(s,z)
generalized Euler sums; 25.16(ii)
(f;x)
Hilbert transform; 1.14(v)
H(z|τ)=θ1(u|τ)
Jacobi’s notation; 20.1
(with θj(z|τ): theta function)
H(a,u)
line-broadening function; (7.19.4)
Hn(x| q)
continuous q-Hermite polynomial; (18.28.16)
hn(x| q)
continuous q-1-Hermite polynomial; (18.28.18)
H1(z|τ)=θ2(u|τ)
Jacobi’s notation; 20.1
(with θj(z|τ): theta function)
hn(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)
Hqp(a1,,apb1,,bq;z)
bilateral hypergeometric function; (16.4.16)
hcpm(z,ξ)
paraboloidal wave function; 28.31(iii)
(s1,s2)Hfm(a,qm;α,β,γ,δ;z)
Heun functions; 31.4
(s1,s2)Hfmν(a,qm;α,β,γ,δ;z)
path-multiplicative solutions of Heun’s equation; 31.6
Hhn(z)
probability function; 12.7(ii)
Hhn(z)
probability function; (7.18.12)
Hi(z)
Scorer function (inhomogeneous Airy function); 9.12(i)
Hiν(z)=Hν(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)
Hpn,m(a,qn,m;-n,β,γ,δ;z)
Heun polynomials; (31.5.2)
Hsν(z)=Hν(1)(z)
notation used by Jeffreys and Jeffreys (1956); 10.1
(with Hν(1)(z): Bessel function of the third kind (or Hankel function))
hspm(z,ξ)
paraboloidal wave function; 28.31(iii)