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Notations D

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𝒟 ( I )
test function space; §1.16(i)
D ( k )
complete elliptic integral of Legendre’s type; 19.2.8
d x
differential of x; §1.4(iv)
d ( n )
divisor function; 27.2.9
d ( n )
derangement number; §26.13
x
partial differential of x; 1.5.3
𝒟 q
q-differential operator; 17.2.41
D ν ( z )
parabolic cylinder function; §12.1
d k ( n )
divisor function; §27.2(i)
d q x
q-differential; §17.2(v)
D α
fractional derivative; 1.15.51
D ( m , n )
Delannoy number; 26.6.1
D ( ϕ , k )
incomplete elliptic integral of Legendre’s type; 19.2.6
𝔇 l m ( θ , ϕ ) Y l , m ( θ , ϕ )
alternative notation; §14.30(i)
(with Yl,m(θ,ϕ): spherical harmonic)
D j ( ν , μ , z )
cross-products of modified Mathieu functions and their derivatives; 28.28.24
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 of f with respect to x; 1.4.4
f x
partial derivative of f with respect to x; 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 ( τ )
discriminant function; 27.14.16
δ ( x - a )
Dirac delta (or Dirac delta function); §1.17(i)
δ x
central difference; §18.1(i)
Δ x
forward difference; §18.1(i)
det
determinant; §1.3(i)
div
divergence of vector-valued function; 1.6.21
dn ( z | m ) = dn ( z , m )
alternative notation; §22.1
(with dn(z,k): Jacobian elliptic function)
dn ( z , k )
Jacobian elliptic function; 22.2.6
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