Notations I

$\mathbf{I}$: identity matrix; (1.2.53)
$\Im$: imaginary part; (1.9.2)
$\mathrm{i}$: imaginary unit; (1.9.1)
$I^{\NVar{\alpha}}$: fractional integral; (1.15.47)
$I(\NVar{\mathbf{m}})$: general elliptic integral; §19.29(ii)
$\widetilde{I}_{\NVar{\nu}}\left(\NVar{x}\right)$: modified Bessel function of the first kind of imaginary order; (10.45.2)
$I_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Bessel function of the first kind; (10.25.2)
${\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$: modified spherical Bessel function; (10.47.7)
${\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$: modified spherical Bessel function; (10.47.8)
$I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)$: incomplete beta function; (8.17.2)
$I(\NVar{a},\NVar{b},\NVar{x})=I_{x}\left(a,b\right)$: notation used by Magnus et al. (1966); §8.1
(with $I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)$ : incomplete beta function)

$\operatorname{idem}\left(\NVar{\chi_{1}};\NVar{\chi_{2},\dots,\chi_{n}}\right)$: $\operatorname{idem}$ function; §17.1
$\operatorname{Ie}_{\NVar{n}}\left(\NVar{z},\NVar{h}\right)$: modified Mathieu function; (28.20.17)
$\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(\NVar{z}\right)$: repeated integrals of the complementary error function; (7.18.2)
$\mathrm{in}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{fe}_{n}\left(z,q\right)$: notation used by Campbell (1955); §28.1
(with $\operatorname{fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : second solution, Mathieu’s equation)
$\inf$: greatest lower bound (infimum); Common Notations and Definitions
$\mathrm{inh}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{Fe}_{n}\left(z,q\right)$: notation used by Campbell (1955); §28.1
(with $\operatorname{Fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : modified Mathieu function)
$\mathrm{inv}$: inversion number; §26.14(i)
$\operatorname{inverf}\NVar{x}$: inverse error function; (7.17.1)
$\operatorname{inverfc}\NVar{x}$: inverse complementary error function; (7.17.1)
$\operatorname{Io}_{\NVar{n}}\left(\NVar{z},\NVar{h}\right)$: modified Mathieu function; (28.20.18)

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