besseli - Modified Bessel functions of the first kind (I sub alpha).
besseli(alpha,x) computes modified Bessel functions of the first kind (I 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 besseli(alpha(j),x(i)) .
I_alpha and K_alpha (see besselk ) 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 (I_alpha_scaled(x) = exp(-x) I_alpha(x)).
// example : display some I bessel functions x = linspace(0.01,10,5000)'; y = besseli(0:4,x); ys = besseli(0:4,x,2); xbasc() subplot(2,1,1) plot2d(x,y, style=2:6, leg="I0@I1@I2@I3@I4", rect=[0,0,6,10]) xtitle("Some modified bessel functions of the first kind") subplot(2,1,2) plot2d(x,ys, style=2:6, leg="I0s@I1s@I2s@I3s@I4s", rect=[0,0,6,1]) xtitle("Some modified scaled bessel functions of the first kind")
W. J. Cody, L. Stoltz (code from Netlib (specfun))