DLMF: Notations D

Notations D

♦*♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

$\mathcal{D}(I)$: test function space; §1.16(i)
$\mathop{D\/}\nolimits\!\left(k\right)$: complete elliptic integral of Legendre’s type; (19.2.8)
$dx$: differential of $x$ ; §1.4(iv)
$\mathop{d\/}\nolimits\!\left(n\right)$: divisor function; (27.2.9)
$d(n)$: derangement number; §26.13
$\partial x$: partial differential of $x$ ; (1.5.3)
$\mathcal{D}_{q}$: $q$ -differential operator; (17.2.41)
$\mathop{D_{{\nu}}\/}\nolimits\!\left(z\right)$: parabolic cylinder function; §12.1
$\mathop{d_{{k}}\/}\nolimits\!\left(n\right)$: divisor function; §27.2(i)
${d}_{q}x$: $q$ -differential; §17.2(v)
$D^{\alpha}$: fractional derivative; (1.15.51)
$D(m,n)$: Dellanoy number; (26.6.1)
$\mathop{D\/}\nolimits\!\left(\phi,k\right)$: incomplete elliptic integral of Legendre’s type; (19.2.6)
$\mathfrak{D}_{{lm}}(\theta,\phi)\propto\mathop{Y_{{{l},{m}}}\/}\nolimits\!\left(\theta,\phi\right)$: alternative notation; §14.30(i)
(with $\mathop{Y_{{{l},{m}}}\/}\nolimits\!\left(\theta,\phi\right)$ : spherical harmonic)
$\mathop{\mathrm{D}_{{j}}\/}\nolimits\!\left(\nu,\mu,z\right)$: cross-products of modified Mathieu functions and their derivatives; (28.28.24)
$\mathop{\mathrm{dc}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.8)
$\mathop{\mathrm{Dc}_{{j}}\/}\nolimits\!\left(n,m,z\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.39)

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ ; (1.4.4)
$\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ ; (1.5.3)
$\frac{\partial(f,g)}{\partial(x,y)}$: Jacobian; (1.5.38)
$\mathop{\mathit{dE}^{{m}}_{{2n+1}}\/}\nolimits\!\left(z,k^{2}\right)$: Lamé polynomial; (29.12.4)
$\Delta$: forward difference operator; §3.6(i)
$\delta _{{j,k}}$: Kronecker delta; Common Notations and Definitions
$\mathop{\Delta\/}\nolimits\!\left(\tau\right)$: discriminant function; (27.14.16)
$\mathop{\delta\/}\nolimits\!\left(x-a\right)$: Dirac delta (or Dirac delta function); §1.17(i)
$\delta _{{x}}$: central difference; ¶ ‣ §18.1(i)
$\Delta _{{x}}$: forward difference; ¶ ‣ §18.1(i)
$\det$: determinant; §1.3(i)
$\divergence$: divergence of vector-valued function; (1.6.21)
$\mathrm{dn}(z\mathpunct{|}m)=\mathop{\mathrm{dn}\/}\nolimits\left(z,\sqrt{m}\right)$: alternative notation; §22.1
(with $\mathop{\mathrm{dn}\/}\nolimits\left(z,k\right)$ : Jacobian elliptic function)
$\mathop{\mathrm{dn}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.6)
$\mathop{\mathrm{ds}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.7)
$\mathop{\mathrm{Ds}_{{j}}\/}\nolimits\!\left(n,m,z\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.35)
$\mathop{\mathrm{Dsc}_{{j}}\/}\nolimits\!\left(n,m,z\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.40)