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Notations

Notations D

𝒟 q
q-differential operator; (17.2.41)
𝐷 α
fractional derivative; (1.15.51)
D ( k )
complete elliptic integral of Legendre’s type; (19.2.8)
d ( n )
divisor function; (27.2.9)
d ( n )
derangement number; §26.13
d x
differential; §1.4(iv)
x
partial differential; (1.5.3)
d k ( n )
divisor function; §27.2(i)
D ν ( z )
parabolic cylinder function; §12.1
d q x
q-differential; §17.2(v)
D ( m , n )
Delannoy number; (26.6.1)
D ( ϕ , k )
incomplete elliptic integral of Legendre’s type; (19.2.6)
D j ( ν , μ , z )
cross-products of modified Mathieu functions and their derivatives; (28.28.24)
𝔇 l m ( θ , ϕ ) Y l , m ( θ , ϕ )
alternative notation; §14.30(i)
(with Yl,m(θ,ϕ): spherical harmonic)
dc ( z , k )
Jacobian elliptic function; (22.2.8)
Dc j ( n , m , z )
cross-products of radial Mathieu functions and their derivatives; (28.28.39)
d f d x
derivative; (1.4.4)
f x
partial derivative; (1.5.3)
( f , g ) ( x , y )
Jacobian; (1.5.38)
𝑑𝐸 2 n + 1 m ( z , k 2 )
Lamé polynomial; (29.12.4)
Δ
forward difference operator; §3.6(i)
δ j , k
Kronecker delta; Common Notations and Definitions
δ x
central difference; §18.1(i)
Δ x
forward difference; §18.1(i)
Δ ( τ )
discriminant function; (27.14.16)
δ x
Dirac delta distribution; §1.16(iii)
δ ( x a )
Dirac delta (or Dirac delta function); §1.17(i)
δ n ( x )
Dirac delta sequence; §1.17(i)
det
determinant; §1.3(i)
div
divergence of vector-valued function; (1.6.21)
dn ( z , k )
Jacobian elliptic function; (22.2.6)
dn ( z | m ) = dn ( z , m )
alternative notation; §22.1
(with dn(z,k): Jacobian elliptic function)
ds ( z , k )
Jacobian elliptic function; (22.2.7)
Ds j ( n , m , z )
cross-products of radial Mathieu functions and their derivatives; (28.28.35)
Dsc j ( n , m , z )
cross-products of radial Mathieu functions and their derivatives; (28.28.40)