Notations E

*ABCD♦E♦FGHIJKLMNOPQRSTUVWXYZ
$\mathrm{e}$
base of exponential function; 4.2.11
$\in$
element of; Common Notations and Definitions
$\notin$
not an element of; Common Notations and Definitions
$E_{\NVar{n}}$
Euler numbers; §24.2(ii)
$\mathop{E^{(\NVar{\ell})}_{\NVar{n}}\/}\nolimits$
generalized Euler numbers; §24.16(i)
$E(\NVar{\alpha})=\mathop{E\/}\nolimits\!\left(k\right)$
notation used by Abramowitz and Stegun (1964, Chapter 17); §19.1
$\mathop{E\/}\nolimits\!\left(\NVar{k}\right)$
Legendre’s complete elliptic integral of the second kind; 19.2.8
$\mathop{\eta\/}\nolimits\!\left(\NVar{\tau}\right)$
Dedekind’s eta function (or Dedekind modular function); 27.14.12
$\mathop{E_{1}\/}\nolimits\!\left(\NVar{z}\right)$
exponential integral; 6.2.1
$\mathop{{E^{\prime}}\/}\nolimits\!\left(\NVar{k}\right)$
Legendre’s complementary complete elliptic integral of the second kind; 19.2.9
$e_{0}(\NVar{x})=\pi\mathop{\mathrm{Hi}\/}\nolimits\!\left(-x\right)$
notation used by Tumarkin (1959); §9.1
$\tilde{e}_{0}(\NVar{x})=-\pi\mathop{\mathrm{Gi}\/}\nolimits\!\left(-x\right)$
notation used by (Tumarkin, 1959); §9.1
$\mathop{E_{\NVar{a},\NVar{b}}\/}\nolimits\!\left(\NVar{z}\right)$
Mittag-Leffler function; 10.46.3
$\mathop{E_{\NVar{n}}\/}\nolimits\!\left(\NVar{x}\right)$
Euler polynomials; §24.2(ii)
$\mathop{\mathbf{E}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$
Weber function; 11.10.2
$\mathop{E_{\NVar{p}}\/}\nolimits\!\left(\NVar{z}\right)$
generalized exponential integral; 8.19.1
$\mathop{E_{\NVar{q}}\/}\nolimits\!\left(\NVar{x}\right)$
$q$-exponential function; 17.3.2
$\mathop{e_{\NVar{q}}\/}\nolimits\!\left(\NVar{x}\right)$
$q$-exponential function; 17.3.1
$E_{\NVar{s}}(\NVar{\mathbf{z}})$
elementary symmetric function; 19.19.4
$\mathop{E^{(\NVar{\ell})}_{\NVar{n}}\/}\nolimits\!\left(\NVar{x}\right)$
generalized Euler polynomials; §24.16(i)
$\mathop{\widetilde{E}_{\NVar{n}}\/}\nolimits\!\left(\NVar{x}\right)$
periodic Euler functions; §24.2(iii)
$E(\NVar{\phi}\backslash\NVar{\alpha})=\mathop{E\/}\nolimits\!\left(\phi,k\right)$
notation used by Abramowitz and Stegun (1964, Chapter 17); §19.1
$\mathop{E\/}\nolimits\!\left(\NVar{\phi},\NVar{k}\right)$
Legendre’s incomplete elliptic integral of the second kind; 19.2.5
${\rm Ec}_{\NVar{\nu}}^{\NVar{2m}}(\NVar{z},\NVar{k^{2}})\propto\mathop{\mathit% {Ec}^{2m}_{\nu}\/}\nolimits\!\left(z,k^{2}\right)$
notation used by Ince (1940b); §29.1
${\rm Ec}_{\NVar{\nu}}^{\NVar{2m+1}}(\NVar{z},\NVar{k^{2}})\propto\mathop{% \mathit{Es}^{2m+1}_{\nu}\/}\nolimits\!\left(z,k^{2}\right)$
notation used by Ince (1940b); §29.1
$\mathop{\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z},\NVar{% k^{2}}\right)$
Lamé function; §29.3(iv)
$\mathop{\mathrm{Ei}\/}\nolimits\!\left(\NVar{x}\right)$
exponential integral; §6.2(i)
$\mathop{\mathrm{Ein}\/}\nolimits\!\left(\NVar{z}\right)$
complementary exponential integral; 6.2.3
$\mathop{\mathrm{el1}\/}\nolimits\!\left(\NVar{x},\NVar{k_{c}}\right)$
Bulirsch’s incomplete elliptic integral of the first kind; 19.2.15
$\mathop{\mathrm{el2}\/}\nolimits\!\left(\NVar{x},\NVar{k_{c}},\NVar{a},\NVar{b% }\right)$
Bulirsch’s incomplete elliptic integral of the second kind; 19.2.12
$\mathop{\mathrm{el3}\/}\nolimits\!\left(\NVar{x},\NVar{k_{c}},\NVar{p}\right)$
Bulirsch’s incomplete elliptic integral of the third kind; 19.2.16
$\mathop{\mathrm{envAi}\/}\nolimits\!\left(\NVar{x}\right)$
envelope of Airy function $\mathop{\mathrm{Ai}\/}\nolimits\!\left(\NVar{x}\right)$; §2.8(iii)
$\mathop{\mathrm{envBi}\/}\nolimits\!\left(\NVar{x}\right)$
envelope of Airy function $\mathop{\mathrm{Bi}\/}\nolimits\!\left(\NVar{x}\right)$; §2.8(iii)
$\mathop{\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{x}\right)$
envelope of Bessel function $\mathop{J_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{x}\right)$; §2.8(iv)
$\mathop{\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{x}\right)$
envelope of Bessel function $\mathop{Y_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{x}\right)$; §2.8(iv)
$\mathop{\mathrm{env}\mskip-1.0mu U\/}\nolimits\!\left(\NVar{c},\NVar{x}\right)$
envelope of parabolic cylinder function $\mathop{U\/}\nolimits\!\left(\NVar{c},\NVar{x}\right)$; §14.15(v)
$\mathop{\mathrm{env}\mskip-1.0mu \overline{U}\/}\nolimits\!\left(\NVar{c},% \NVar{x}\right)$
envelope of parabolic cylinder function $\mathop{\overline{U}\/}\nolimits\!\left(\NVar{c},\NVar{x}\right)$; §14.15(v)
$\epsilon_{\NVar{j}\NVar{k}\NVar{\ell}}$
Levi-Civita symbol; 1.6.14
$\mathop{\mathcal{E}\/}\nolimits\!\left(\NVar{x},\NVar{k}\right)$
Jacobi’s epsilon function; 22.16.14
$\operatorname{Erf}\NVar{z}=\tfrac{1}{2}\sqrt{\pi}\mathop{\mathrm{erf}\/}\nolimits z$
alternative notation for the error function; §7.1
$\mathop{\mathrm{erf}\/}\nolimits\NVar{z}$
error function; 7.2.1
$\mathop{\mathrm{erfc}\/}\nolimits\NVar{z}$
complementary error function; 7.2.2
$\operatorname{Erfi}\NVar{z}=e^{z^{2}}\mathop{F\/}\nolimits\!\left(z\right)$
alternative notation for Dawson’s integral; §7.1
${\rm Es}_{\NVar{\nu}}^{\NVar{2m+1}}(\NVar{z},\NVar{k^{2}})\propto\mathop{% \mathit{Ec}^{2m+1}_{\nu}\/}\nolimits\!\left(z,k^{2}\right)$
notation used by Ince (1940b); §29.1
${\rm Es}_{\NVar{\nu}}^{\NVar{2m+2}}(\NVar{z},\NVar{k^{2}})\propto\mathop{% \mathit{Es}^{2m+2}_{\nu}\/}\nolimits\!\left(z,k^{2}\right)$
notation used by Ince (1940b); §29.1
$\mathop{\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z},\NVar{% k^{2}}\right)$
Lamé function; §29.3(iv)
$\mathop{\mathrm{etr}\/}\nolimits\!\left(\NVar{\mathbf{X}}\right)$
exponential of trace; §35.1
$\mathop{\exp\/}\nolimits\NVar{z}$
exponential function; 4.2.19