Notations D

$\mathcal{D}_{\NVar{q}}$: $q$ -differential operator; (17.2.41)
$D^{\NVar{\alpha}}$: fractional derivative; (1.15.51)
$D\left(\NVar{k}\right)$: complete elliptic integral of Legendre’s type; (19.2.8)
$d\left(\NVar{n}\right)$: divisor function; (27.2.9)
$d(\NVar{n})$: derangement number; §26.13
$\,\mathrm{d}\NVar{x}$: differential of $x$ ; §1.4(iv)
$\,\partial\NVar{x}$: partial differential of $x$ ; (1.5.3)
$d_{\NVar{k}}\left(\NVar{n}\right)$: divisor function; §27.2(i)
$\operatorname{Disc}\left(\NVar{x}\right)$: discriminant function; (18.2.20)
$D_{\NVar{\nu}}\left(\NVar{z}\right)$: parabolic cylinder function; §12.1
$\,{\mathrm{d}}_{\NVar{q}}\NVar{x}$: $q$ -differential; §17.2(v)
$D(\NVar{m},\NVar{n})$: Delannoy number; (26.6.1)
$D\left(\NVar{\phi},\NVar{k}\right)$: incomplete elliptic integral of Legendre’s type; (19.2.6)
$\operatorname{D}_{\NVar{j}}\left(\NVar{\nu},\NVar{\mu},\NVar{z}\right)$: cross-products of modified Mathieu functions and their derivatives; (28.28.24)
$\mathfrak{D}_{\NVar{lm}}(\NVar{\theta},\NVar{\phi})\propto Y_{{l},{m}}\left(% \theta,\phi\right)$: alternative notation; §14.30(i)
(with $Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},\NVar{\phi}\right)$ : spherical harmonic)
$\operatorname{dc}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.8)
$\operatorname{Dc}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.39)
$\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$: derivative of $f$ with respect to $x$ ; (1.4.4)

$\frac{\partial\NVar{f}}{\partial\NVar{x}}$: partial derivative of $f$ with respect to $x$ ; (1.5.3)
$\frac{\partial(\NVar{f,g})}{\partial(\NVar{x,y})}$: Jacobian; (1.5.38)
$\mathit{dE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z},\NVar{k^{2}}\right)$: Lamé polynomial; (29.12.4)
$\Delta$: forward difference operator; §3.6(i)
$\delta_{\NVar{j},\NVar{k}}$: Kronecker delta; Common Notations and Definitions
$\delta_{\NVar{x}}$: central difference; §18.1(i)
$\Delta_{\NVar{x}}$: forward difference; §18.1(i)
$\Delta\left(\NVar{\tau}\right)$: discriminant function; (27.14.16)
$\delta_{x}$: Dirac delta distribution; §1.16(iii)
$\delta\left(\NVar{x-a}\right)$: Dirac delta (or Dirac delta function); §1.17(i)
$\delta_{n}\left(\NVar{x}\right)$: Dirac delta sequence; §1.17(i)
$\det$: determinant; §1.2(vi)
$\operatorname{div}$: divergence of vector-valued function; (1.6.21)
$\operatorname{dn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.6)
$\mathrm{dn}(\NVar{z}\mathpunct{|}\NVar{m})=\operatorname{dn}\left(z,\sqrt{m}\right)$: alternative notation; §22.1
(with $\operatorname{dn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function)
$\operatorname{ds}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.7)
$\operatorname{Ds}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.35)
$\operatorname{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)$: cross-products of radial Mathieu functions and their derivatives; (28.28.40)

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