Scilab Function
Last update : September 1997

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

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

oldbesselk - Modified Bessel functions of the second kind (K sub alpha).

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

Calling Sequence

y = oldbesseli(alpha,x)
y = oldbesseli(alpha,x,ice)
y = oldbesselj(alpha,x)
y = oldbesselj(alpha,x,ice)
y = oldbesselk(alpha,x)
y = oldbesselk(alpha,x,ice)
y = oldbessely(alpha,x)
y = oldbessely(alpha,x,ice)

Parameters

Description

these functions are obsolete, use besseli , besselj , besselk , bessely instead. Note however that the semantics of these two functions are different.

oldbesseli(alpha,x) computes modified Bessel functions of the first kind (I sub alpha), for real, non-negative order alpha and real argument x . oldbesseli(alpha,x,2) computes oldbesseli(alpha,x).*exp(-abs(real(x))) .

oldbesselj(alpha,x) computes Bessel functions of the first kind (J sub alpha), for real, non-negative order alpha and real argument x . oldbesselj(alpha,x,2) computes oldbesselj(alpha,x).*exp(-abs(imag(x))) .

oldbesselk(alpha,x) computes modified Bessel functions of the second kind (K sub alpha), for real, non-negative order alpha and real argument x . oldbesselk(alpha,x,1) computes oldbesselk(alpha,x).*exp(x)

oldbessely(alpha,x) computes Bessel functions of the second kind (Y sub alpha), for real, non-negative order alpha and real argument x . oldbessely(alpha,x,1) computes oldbessely(alpha,x).*exp(-abs(imag(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 oldbesseli(alpha(j),x(i)) .

I_alpha and K_alpha are 2 independant solutions of the modified Bessel's differential equation :


          2                     2        2
         x  y(x)" + x y(x)' - (x  + alpha ) y(x) = 0 , 
     
    

J_alpha and Y_alpha are 2 independant solutions of the Bessel's differential equation :


          2                     2        2
         x  y(x)" + x y(x)' + (x  - alpha ) y(x) = 0 , 
     
    

Examples


// example : display some I bessel functions
x = linspace(0.01,10,5000)';
y = oldbesseli(0:4,x);
ys = oldbesseli(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")
 
  

Author

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