Notations K

$K(\NVar{\alpha})=K\left(k\right)$: notation used by Abramowitz and Stegun (1964, Chapter 17); §19.1
(with $K\left(\NVar{k}\right)$ : Legendre’s complete elliptic integral of the first kind)
$K\left(\NVar{k}\right)$: Legendre’s complete elliptic integral of the first kind; (19.2.8)
${K^{\prime}}\left(\NVar{k}\right)$: Legendre’s complementary complete elliptic integral of the first kind; (19.2.8_1)
$\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)$: modified spherical Bessel function; (10.47.9)
$\mathcal{K}_{\NVar{\nu}}(\NVar{\mathbf{T}})=\left|\mathbf{T}\right|^{\nu}B_{% \nu}\left(\mathbf{S}\mathbf{T}\right)$: notation used by Faraut and Korányi (1994, pp. 357–358); §35.1
(with $B_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$ : Bessel function of matrix argument (second kind))
$\widetilde{K}_{\NVar{\nu}}\left(\NVar{x}\right)$: modified Bessel function fo the second kind of imaginary order; (10.45.2)
$K_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Bessel function of the second kind; (10.25.3)
$\mathbf{K}_{\NVar{\nu}}\left(\NVar{z}\right)$: Struve function; (11.2.5)
$K_{\NVar{\nu}}(\NVar{z})=\cos\left(\NVar{\nu}\pi\right)K_{\nu}\left(z\right)$: notation used by Whittaker and Watson (1927); §10.1
(with $\pi$ : the ratio of the circumference of a circle to its diameter, $\cos\NVar{z}$ : cosine function and $K_{\NVar{\nu}}\left(\NVar{z}\right)$ : modified Bessel function of the second kind)
$\mathfrak{K}(\NVar{a},\NVar{x},\NVar{s})=\Phi\left(e^{2\pi ix},s,a\right)$: notation used by (Lerch, 1887); §25.14(i)
(with $\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)$ : Lerch’s transcendent, $\pi$ : the ratio of the circumference of a circle to its diameter, $\mathrm{e}$ : base of natural logarithm and $\mathrm{i}$ : imaginary unit)

$K_{\NVar{m}}(\NVar{0},\NVar{\dots},\NVar{0},\NVar{\nu}\mathpunct{|}\NVar{% \mathbf{S}},\NVar{\mathbf{T}})=\left|\mathbf{T}\right|^{\nu}B_{\nu}\left(% \mathbf{S}\mathbf{T}\right)$: notation used by Terras (1988, pp. 49–64); §35.1
(with $B_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$ : Bessel function of matrix argument (second kind))
$K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}\right)$: Krawtchouk polynomial; Table 18.19.1
$\kappa(\NVar{\lambda})$: condition number; §3.2(v)
$\operatorname{Ke}_{\NVar{n}}\left(\NVar{z},\NVar{h}\right)$: modified Mathieu function; (28.20.19)
$\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)$: Kelvin function; (10.61.2)
$\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)$: Kelvin function; (10.61.2)
$\mathrm{Kh}_{\NVar{\nu}}(\NVar{z})=(2/\pi)K_{\nu}\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with $\pi$ : the ratio of the circumference of a circle to its diameter and $K_{\NVar{\nu}}\left(\NVar{z}\right)$ : modified Bessel function of the second kind)
$\operatorname{Ki}_{\NVar{\alpha}}\left(\NVar{x}\right)$: Bickley function; (10.43.11)
$\operatorname{Ko}_{\NVar{n}}\left(\NVar{z},\NVar{h}\right)$: modified Mathieu function; (28.20.20)

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