Notations M

$m_{e}$: mass of electron; §18.39(ii)
$M(\NVar{n})$: Motzkin number; (26.6.2)
$\mathsf{M}\left(\NVar{x}\right)$: Mills’ ratio; (7.8.1)
$M\left(\NVar{z}\right)$: Airy modulus function; (9.8.3)
$\mathscr{M}_{\NVar{\kappa},\NVar{\mu}}=M_{\kappa,\mu}\left(z\right)/\Gamma% \left(1+2\mu\right)$: notation used by Buchholz (1969); §13.1
(with $\Gamma\left(\NVar{z}\right)$ : gamma function and $M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)$ : Whittaker confluent hypergeometric function)
$M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)$: Whittaker confluent hypergeometric function; (13.14.2)
$M_{\NVar{\nu}}\left(\NVar{x}\right)$: modulus of Bessel functions; (10.18.1)
$\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Struve function; (11.2.6)
$M\left(\NVar{a},\NVar{g}\right)$: arithmetic-geometric mean; §19.8(i)
$\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)$: Mellin transform; (1.14.32)
$M_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}\right)$: envelope of Coulomb functions; (33.3.1)
${\operatorname{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{z},\NVar{h}\right)$: modified Mathieu function; §28.20(iii)

$M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function; (13.2.2)
${\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Olver’s confluent hypergeometric function; (13.2.3)
$M_{\NVar{n}}\left(\NVar{x};\NVar{\beta},\NVar{c}\right)$: Meixner polynomial; Table 18.19.1
$\mathrm{maj}$: major index; §26.14(i)
${\operatorname{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)$: radial Mathieu function; (28.20.15)
$\operatorname{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$: Mathieu function; §28.12(ii)
$\operatorname{me}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$: Mathieu function of noninteger order; §28.12(ii)
$\operatorname{Me}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$: modified Mathieu function; (28.20.5)
$\mathrm{Me}_{\NVar{n}}^{(1,2)}(\NVar{z},\NVar{q})=\sqrt{\tfrac{1}{2}\pi}g_{% \mathit{e},n}(h)\operatorname{ce}_{n}\left(0,q\right){\operatorname{Mc}^{(3,4)% }_{n}}\left(z,h\right)$: notation used by Arscott (1964b), McLachlan (1947); §28.1
(with $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter and ${\operatorname{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)$ : radial Mathieu function)
$\mod$: modulo; Common Notations and Definitions
${\operatorname{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)$: radial Mathieu function; (28.20.16)
$\mu\left(\NVar{n}\right)$: Möbius function; (27.2.12)

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Notations M

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