DLMF: Notations K

Notations K

♦*♦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♦

$K(\alpha)=\mathop{K\/}\nolimits\!\left(k\right)$: notation used by Abramowitz and Stegun (1964, Chapter 17); §19.1
(with $\mathop{K\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the first kind)
$\mathop{K\/}\nolimits\!\left(k\right)$: Legendre’s complete elliptic integral of the first kind; (19.2.8)
$\kappa(\lambda)$: condition number; §3.2(v)
$\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$: modified Bessel function; (10.25.3)
$\mathop{\widetilde{K}_{{\nu}}\/}\nolimits\!\left(x\right)$: modified Bessel function of imaginary order; (10.45.2)
$\mathcal{K}_{\nu}(\mathbf{T})=|\mathbf{T}|^{\nu}\mathop{B_{{\nu}}\/}\nolimits\!\left(\mathbf{S}\mathbf{T}\right)$: notation used by Faraut and Korányi (1994, pp. 357–358); §35.1
(with $\mathop{B_{{\nu}}\/}\nolimits\!\left(\mathbf{T}\right)$ : Bessel function of matrix argument (second kind))
$\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$: Struve function; (11.2.5)
$K_{\nu}(z)=\mathop{\cos\/}\nolimits(\nu\pi)\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$: notation used by Whittaker and Watson (1927); §10.1
(with $\mathop{\cos\/}\nolimits z$ : cosine function and $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function)
$\mathop{\mathsf{k}_{{n}}\/}\nolimits\!\left(z\right)$: modified spherical Bessel function; (10.47.9)
$\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$: Legendre’s complementary complete elliptic integral of the first kind; (19.2.9)

$\mathfrak{K}(a,x,s)=\mathop{\Phi\/}\nolimits\!\left(e^{{2\pi ix}},s,a\right)$: notation used by (Lerch, 1887); §25.14(i)
(with $\mathop{\Phi\/}\nolimits\!\left(z,s,a\right)$ : Lerch’s transcendent and $e$ : base of exponential function)
$\mathop{K_{{n}}\/}\nolimits\!\left(x;p,N\right)$: Krawtchouk polynomial; Table 18.19.1
$K_{m}(0,\dots,0,\nu\mathpunct{|}\mathbf{S},\mathbf{T})=|\mathbf{T}|^{\nu}\mathop{B_{{\nu}}\/}\nolimits\!\left(\mathbf{S}\mathbf{T}\right)$: notation used by Terras (1988, pp. 49–64); §35.1
(with $\mathop{B_{{\nu}}\/}\nolimits\!\left(\mathbf{T}\right)$ : Bessel function of matrix argument (second kind))
$\mathop{\mathrm{Ke}_{{n}}\/}\nolimits\!\left(z,h\right)$: modified Mathieu function; (28.20.19)
$\mathop{\mathrm{kei}_{{\nu}}\/}\nolimits\!\left(x\right)$: Kelvin function; (10.61.2)
$\mathop{\mathrm{ker}_{{\nu}}\/}\nolimits\!\left(x\right)$: Kelvin function; (10.61.2)
$\mathrm{Kh}_{\nu}(z)=(2/\pi)\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$: notation used by Jeffreys and Jeffreys (1956); §10.1
(with $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function)
$\mathop{\mathrm{Ki}_{{\alpha}}\/}\nolimits\!\left(x\right)$: Bickley function; (10.43.11)
$\mathop{\mathrm{Ko}_{{n}}\/}\nolimits\!\left(z,h\right)$: modified Mathieu function; (28.20.20)