Man Scilab

besselj - Bessel functions of the first kind (J sub alpha).

Calling Sequence

y = besselj(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

besselj(alpha,x) computes Bessel functions of the first kind (J 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 besselj(alpha(j),x(i)) .

J_alpha and Y_alpha (see bessely ) 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 #1 : display some bessel functions
x = linspace(0,40,5000)';
y = besselj(0:4,x);
xbasc()
plot2d(x,y, style=2:6, leg="J0@J1@J2@J3@J4")
xtitle("Some bessel functions of the first kind")

// example #2 : use the fact that J_(1/2)(x) = sqrt(2/(x pi)) sin(x)
//              to compare the algorithm of besselj(0.5,x) with
//              a more direct formula 
x = linspace(0.1,40,5000)';
y1 = besselj(0.5, x);
y2 = sqrt(2 ./(%pi*x)).*sin(x);
er = abs((y1-y2)./y2);
ind = find(er > 0 & y2 ~= 0);
xbasc()
subplot(2,1,1)
   plot2d(x,y1,style=2)
   xtitle("besselj(0.5,x)")
subplot(2,1,2)
   plot2d(x(ind), er(ind), style=2, logflag="nl")
   xtitle("relative error between 2 formulae for besselj(0.5,x)") 
 
  

See Also

besseli ,   besselk ,   bessely ,  

Author

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

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