bessely - Bessel functions of the second kind (Y sub alpha).
bessely(alpha,x) computes Bessel functions of the second kind (Y 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 bessely(alpha(j),x(i)) .
Y_alpha and J_alpha (see besselj ) Bessel functions are 2 independant solutions of the Bessel 's differential equation :
2 2 2 x y" + x y' + (x - alpha ) y = 0 , alpha >= 0
// example : plot severals Y bessels functions x = linspace(0.1,40,5000)'; // Y Bessel functions are unbounded for x -> 0+ y = bessely(0:4,x); xbasc() plot2d(x,y, style=2:6, leg="Y0@Y1@Y2@Y3@Y4", rect=[0,-1.5,40,0.6]) xtitle("Some bessel functions of the second kind")
W. J. Cody (code from Netlib (specfun))