Notations

Notations Q

ℚ
set of all rational numbers; Common Notations and Definitions
Q ⁡ ( z ) = 1 2 ⁢ erfc ⁡ ( z / 2 )
alternative notation for the complementary error function; §7.1
(with erfc⁡z: complementary error function)
𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x )
Ferrers function of the second kind; §14.2(ii)
(with 𝖰νμ⁡(x): Ferrers function of the second kind)
𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z )
Olver’s associated Legendre function; §14.2(ii)
(with 𝑸νμ⁡(z): Olver’s associated Legendre function)
Q z ⁡ ( a ) = Γ ⁡ ( a , z )
notation used by Batchelder (1967, p. 63); §8.1
(with Γ⁡(a,z): incomplete gamma function)
𝖰 ^ − 1 2 + i ⁢ τ − μ ⁡ ( x )
conical function; (14.20.2)
Q ν μ ⁡ ( x ) = 𝖰 ν μ ⁡ ( x )
notation used by Erdélyi et al. (1953a), Olver (1997b); §14.1
(with 𝖰νμ⁡(x): Ferrers function of the second kind)
𝖰 ν μ ⁡ ( x )
Ferrers function of the second kind; (14.3.2)
Q ν μ ⁡ ( x ) = 𝖰 ν μ ⁡ ( x )
notation used by Magnus et al. (1966); §14.1
(with 𝖰νμ⁡(x): Ferrers function of the second kind)
Q ν μ ⁡ ( z )
associated Legendre function of the second kind; §14.21(i)
𝔔 ν μ ⁡ ( z ) = Q ν μ ⁡ ( z )
notation used by Magnus et al. (1966); §14.1
(with Qνμ⁡(z): associated Legendre function of the second kind)
𝑸 ν μ ⁡ ( z )
Olver’s associated Legendre function; §14.21(i)
Q ⁡ ( a , z )
normalized incomplete gamma function; (8.2.4)
Q ℓ ⁡ ( ϵ , r ) = − ( 2 ⁢ ℓ + 1 ) ! ⁢ h ⁡ ( ϵ , ℓ ; r ) / ( 2 ℓ + 1 ⁢ A ⁡ ( ϵ , ℓ ) )
notation used by Curtis (1964a); item Curtis (1964a):
(with h⁡(ϵ,ℓ;r): irregular Coulomb function and !: factorial (as in n!))
Q n ( λ ) ⁡ ( x ; a , b , c )
Pollaczek polynomial; (18.35.2_2)
Q n ⁡ ( x ; a , b | q − 1 )
q−1-Al-Salam–Chihara polynomial; (18.28.9)
Q n ⁡ ( x ; α , β , N )
Hahn polynomial; Table 18.19.1
Q n ⁡ ( x ; α , β , N ; q )
q-Hahn polynomial; (18.27.3)
qs n m ⁡ ( x , γ 2 ) = 𝖰𝗌 n m ⁡ ( x , γ 2 )
notation used by Meixner and Schäfke (1954) for the spheroidal wave function of the second kind; §30.1
(with 𝖰𝗌nm⁡(x,γ2): spheroidal wave function of the second kind)
𝖰𝗌 n m ⁡ ( x , γ 2 )
spheroidal wave function of the second kind; §30.5
Qs n m ⁡ ( z , γ 2 ) = 𝑄𝑠 n m ⁡ ( z , γ 2 )
notation used by Meixner and Schäfke (1954) for the spheroidal wave function of complex argument; §30.1
(with 𝑄𝑠nm⁡(z,γ2): spheroidal wave function of complex argument)
𝑄𝑠 n m ⁡ ( z , γ 2 )
spheroidal wave function of complex argument; §30.6