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Notations

Notations G

*ABCDEF♦G♦HIJKLMNOPQRSTUVWXYZ
G n
Genocchi numbers; §24.15(i)
G ( k )
Waring’s function; §27.13(iii)
g ( k )
Waring’s function; §27.13(iii)
g ( z )
auxiliary function for Fresnel integrals; (7.2.11)
g ( z )
auxiliary function for sine and cosine integrals; (6.2.18)
G ( z )
Barnes’ G-function (or double gamma function); (5.17.1)
G ( z )
Goodwin–Staton integral; (7.2.12)
g e , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
g o , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
G p ( z )
rescaled terminant function; (9.7.22)
G s ( x )
Bose–Einstein integral; (25.12.15)
G ( n , χ )
Gauss sum; (27.10.9)
g j
Weierstrass lattice invariants g2, g3; §23.3(i)
G ( η , ρ )
irregular Coulomb radial function; (33.2.11)
g ( ϵ , ; r ) = c ( ϵ , ; r )
notation used by Greene et al. (1979); item Greene et al. (1979):
(with c(ϵ,;r): irregular Coulomb function)
G n ( p , q , x )
shifted Jacobi polynomial; (18.1.2)
Gp,qm,n(z;a1,,apb1,,bq) or Gp,qm,n(z;a;b)
Meijer G-function; (16.17.1)
γ
Euler’s constant; (5.2.3)
Γ ( z )
gamma function; (5.2.1)
Γ m ( a )
multivariate gamma function; §35.3(i)
Γ q ( z )
q-gamma function; (5.18.4)
Γ ( a , z )
incomplete gamma function; (8.2.2)
γ * ( a , z )
incomplete gamma function; (8.2.6)
gd x
Gudermannian function; (4.23.39)
gd - 1 ( x )
inverse Gudermannian function; (4.23.41)
Ge n ( z , q )
modified Mathieu function; (28.20.7)
ge n ( z , q )
second solution, Mathieu’s equation; (28.5.2)
Gey n ( z , q ) = 1 2 π g o , n ( h ) se n ( 0 , q ) Ms n ( 2 ) ( z , h )
notation used by Arscott (1964b), McLachlan (1947); §28.1
(with sen(z,q): Mathieu function, π: the ratio of the circumference of a circle to its diameter and Msn(j)(z,h): radial Mathieu function)
Gi ( z )
Scorer function (inhomogeneous Airy function); (9.12.4)
grad
gradient of differentiable scalar function; (1.6.20)