Digital Library of Mathematical Functions
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Notations

Notations K

*ABCDEFGHIJ♦K♦LMNOPQRSTUVWXYZ
K(α)=K(k)
notation used by Abramowitz and Stegun (1964, Chapter 17); 19.1
(with K(k): Legendre’s complete elliptic integral of the first kind)
K(k)
Legendre’s complete elliptic integral of the first kind; (19.2.8)
κ(λ)
condition number; 3.2(v)
Kν(z)
modified Bessel function; (10.25.3)
K~ν(x)
modified Bessel function of imaginary order; (10.45.2)
𝒦ν(T)=|T|νBν(ST)
notation used by Faraut and Korányi (1994, pp. 357–358); 35.1
(with Bν(T): Bessel function of matrix argument (second kind))
Kν(z)
Struve function; (11.2.5)
Kν(z)=cos(νπ)Kν(z)
notation used by Whittaker and Watson (1927); 10.1
(with cosz: cosine function and Kν(z): modified Bessel function)
kn(z)
modified spherical Bessel function; (10.47.9)
K(k)
Legendre’s complementary complete elliptic integral of the first kind; (19.2.9)
𝔎(a,x,s)=Φ(2πx,s,a)
notation used by (Lerch, 1887); 25.14(i)
(with Φ(z,s,a): Lerch’s transcendent and : base of exponential function)
Kn(x;p,N)
Krawtchouk polynomial; 18.19.1
Km(0,,0,ν|S,T)=|T|νBν(ST)
notation used by Terras (1988, pp. 49–64); 35.1
(with Bν(T): Bessel function of matrix argument (second kind))
Ken(z,h)
modified Mathieu function; (28.20.19)
keiν(x)
Kelvin function; (10.61.2)
kerν(x)
Kelvin function; (10.61.2)
Khν(z)=(2/π)Kν(z)
notation used by Jeffreys and Jeffreys (1956); 10.1
(with Kν(z): modified Bessel function)
Kiα(x)
Bickley function; (10.43.11)
Kon(z,h)
modified Mathieu function; (28.20.20)