DLMF: Notations L

Notations L

♦*♦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♦

$\mathbb{L}$: lattice in $\Complex$ ; §23.2(i)
$L_{n}$: Lebesgue constant; (1.8.8)
$\mathop{L_{{n}}\/}\nolimits\!\left(x\right)$: Laguerre polynomial; ¶ ‣ §18.1(ii)
$\mathop{L_{{n}}\/}\nolimits\!\left(x\right)$: Laguerre polynomial; Table 18.3.1
$\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(z\right)$: modified Struve function; (11.2.2)
$\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x\right)$: Laguerre (or generalized Laguerre) polynomial; Table 18.3.1
$\mathop{L\/}\nolimits\!\left(s,\chi\right)$: Dirichlet $\mathop{L\/}\nolimits$ -function; (25.15.1)
$\mathop{\mathscr{L}\/}\nolimits\left(f;s\right)$: Laplace transform; (1.14.17)
$L_{{c\nu}}^{{(2m)}}(\psi,{k^{{\prime}}}^{2})=(-1)^{m}\mathop{\mathit{Ec}^{{2m}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$: notation used by Jansen (1977); §29.1
(with $\mathop{\mathit{Ec}^{{m}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$ : Lamé function)
$L_{{s\nu}}^{{(2m+1)}}(\psi,{k^{{\prime}}}^{2})=(-1)^{m}\mathop{\mathit{Ec}^{{2m+1}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$: notation used by Jansen (1977); §29.1
(with $\mathop{\mathit{Ec}^{{m}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$ : Lamé function)
$L_{{c\nu}}^{{(2m+1)}}(\psi,{k^{{\prime}}}^{2})=(-1)^{m}\mathop{\mathit{Es}^{{2m+1}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$: notation used by Jansen (1977); §29.1
(with $\mathop{\mathit{Es}^{{m}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$ : Lamé function)
$L_{{s\nu}}^{{(2m+2)}}(\psi,{k^{{\prime}}}^{2})=(-1)^{m}\mathop{\mathit{Es}^{{2m+2}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$: notation used by Jansen (1977); §29.1
(with $\mathop{\mathit{Es}^{{m}}_{{\nu}}\/}\nolimits\!\left(z,k^{2}\right)$ : Lamé function)
$\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x;q\right)$: $q$ -Laguerre polynomial; (18.27.15)
$\mathop{\lambda\/}\nolimits\!\left(\tau\right)$: elliptic modular function; (23.15.6)

$\mathop{\Lambda\/}\nolimits\!\left(n\right)$: Mangoldt’s function; (27.2.14)
$\mathop{\lambda\/}\nolimits\!\left(n\right)$: Liouville’s function; (27.2.13)
$\lambda _{{mn}}(\gamma)=\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)+\gamma^{2}$: alternative notation for eigenvalues of the spheroidal differential equation; ¶ ‣ §30.1
(with $\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ : eigenvalues of the spheroidal differential equation)
$\mathop{\lambda _{{\nu+2n}}\/}\nolimits\!\left(q\right)$: eigenvalues of Mathieu equation; §28.12(i)
$\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$: eigenvalues of the spheroidal differential equation; §30.3(i)
$\mathop{\mathrm{li}\/}\nolimits\!\left(x\right)$: logarithmic integral; (6.2.8)
$\mathop{\mathrm{Li}_{2}\/}\nolimits\!\left(z\right)$: dilogarithm; (25.12.1)
$\mathop{\mathrm{Li}_{{s}}\/}\nolimits\!\left(z\right)$: polylogarithm; (25.12.10)
$\liminf$: least limit point; Common Notations and Definitions
$\mathop{\mathrm{Ln}\/}\nolimits z$: general logarithm function; (4.2.1)
$\mathop{\ln\/}\nolimits z$: principal branch of logarithm function; (4.2.2)
$\mathop{\mathrm{log}\/}\nolimits x$: logarithm to base $e$ (Chapter 27 only); §4.2(ii)
$\mathop{\mathrm{log}_{{10}}\/}\nolimits z$: common logarithm; §4.2(ii)
$\mathop{\mathrm{log}_{{a}}\/}\nolimits z$: logarithm to general base $a$ ; §4.2(ii)