Scilab Function

bessely - Bessel functions of the second kind (Y sub alpha).

### Calling Sequence

  `y = bessely(alpha,x)`

### Parameters

- `x` : real vector with non negative entries
- `alpha` : real vector with non negative entries regularly spaced with increment equal to one `alpha=alpha0+(n1:n2)`

### Description

`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

### Examples

    // 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")

### See Also

`besselj` , `besseli` , `besselk` ,

### Author

W. J. Cody (code from Netlib (specfun))