Man Scilab

besseli - Modified Bessel functions of the first kind (I sub alpha).

Calling Sequence

y = besseli(alpha,x)

y = besseli(alpha,x,ice)

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)
• ice : integer flag, with default value 1

Description

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)).

Examples

// 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")
 
  

See Also

besselj ,   besselk ,   bessely ,  

Author

W. J. Cody, L. Stoltz (code from Netlib (specfun))

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