Man Scilab

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))

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