Modified Bessel function of second kind
K = besselk(nu,Z)
K = besselk(nu,Z,1)
K = besselk(nu,Z) computes
the modified Bessel function of the second kind, Kν(z),
for each element of the array
Z. The order
not be an integer, but must be real. The argument
be complex. The result is real where
Z is positive.
Z are arrays
of the same size, the result is also that size. If either input is
a scalar, it is expanded to the other input's size.
K = besselk(nu,Z,1) computes
Create a column vector of domain values.
z = (0:0.2:1)';
Calculate the function values using
nu = 1.
format long besselk(1,z)
ans = 6×1 Inf 4.775972543220472 2.184354424732687 1.302834939763502 0.861781634472180 0.601907230197235
Define the domain.
X = 0:0.01:5;
Calculate the first five modified Bessel functions of the second kind.
K = zeros(5,501); for i = 0:4 K(i+1,:) = besselk(i,X); end
Plot the results.
plot(X,K,'LineWidth',1.5) axis([0 5 0 8]) grid on legend('K_0','K_1','K_2','K_3','K_4','Location','Best') title('Modified Bessel Functions of the Second Kind for v = 0,1,2,3,4') xlabel('X') ylabel('K_v(X)')
The differential equation
where ν is a real constant, is called the modified Bessel's equation, and its solutions are known as modified Bessel functions.
A solution Kν(z) of the second kind can be expressed as:
where Iν(z) and I–ν(z) form a fundamental set of solutions of the modified Bessel's equation,
and Γ(a) is the gamma function. Kν(z) is independent of Iν(z).
be computed using
This function fully supports tall arrays. For more information, see Tall Arrays.