Notations N

$\cap$: intersection; Common Notations and Definitions
$\mathbb{N}$: set of all positive integers; Common Notations and Definitions
$\mathcal{N}$: winding number; (1.9.32)
$N\left(\NVar{z}\right)$: Airy modulus function; (9.8.7)
$N_{\NVar{\nu}}\left(\NVar{x}\right)$: modulus of derivatives of Bessel functions; (10.18.2)
$N_{\NVar{\nu}}(\NVar{z})=Y_{\nu}\left(z\right)$: common alternative notation; §10.1
(with $Y_{\NVar{\nu}}\left(\NVar{z}\right)$ : Bessel function of the second kind)
$N(\NVar{n},\NVar{k})$: Narayana number; (26.6.3)

$\nabla_{\NVar{x}}$: backward difference; §18.1(i)
$\operatorname{nc}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.5)
$\operatorname{nd}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.6)
$\mathrm{Ne}_{\NVar{n}}^{(1,2)}(\NVar{z},\NVar{q})=\sqrt{\tfrac{1}{2}\pi}g_{% \mathit{o},n}(h)\operatorname{se}_{n}'\left(0,q\right){\operatorname{Ms}^{(3,4% )}_{n}}\left(z,h\right)$: notation used by Arscott (1964b), McLachlan (1947); §28.1
(with $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter and ${\operatorname{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)$ : radial Mathieu function)
$\operatorname{ns}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.4)
$\nu\left(\NVar{n}\right)$: number of distinct primes dividing a number; §27.2(i)