besselk - Modified Bessel functions of the second kind (K sub alpha).
besselk(alpha,x) computes modified Bessel functions of the second kind (K sub alpha), for real, non-negative order alpha and argument x . alpha and x may be vectors. The output is m -by- n with m = size(x,'*') , n = size(alpha,'*') whose (i,j) entry is besselk(alpha(j),x(i)) .
K_alpha and I_alpha (see besseli ) modified Bessel functions are 2 independant solutions of the modified Bessel 's differential equation :
2 2 2 x y" + x y' - (x + alpha ) y = 0 , alpha >= 0
If ice is equal to 2 exponentialy scaled Bessel functions is computed (K_alpha_scaled(x) = exp(x) K_alpha(x)).
// example : display some K bessel functions x = linspace(0.01,10,5000)'; y = besselk(0:4,x); ys = besselk(0:4,x,2); xbasc() subplot(2,1,1) plot2d(x,y, style=2:6, leg="K0@K1@K2@K3@K4", rect=[0,0,6,10]) xtitle("Some modified bessel functions of the second kind") subplot(2,1,2) plot2d(x,ys, style=2:6, leg="K0s@K1s@K2s@K3s@K4s", rect=[0,0,6,10]) xtitle("Some modified scaled bessel functions of the second kind")
W. J. Cody, L. Stoltz (code from Netlib (specfun))