Besseli Function

[Jose Otavio Bueno]

I'm having problems with the Besseli Functions in Octave. While with 
Mathlab it is possible to solve the besseli functions with values up to 
700, with Octave the function returns a valid answer just for input 
values below 81:


OCTAVE:

octave:1> besseli(0,1)
ans = 1.2661
octave:2> besseli(0,10)
ans = 2815.7
octave:3> besseli(0,81)
ans =  6.6864e+33
octave:4> besseli(0,82)
ans = Inf + Infi
octave:5> besseli(0,700)
ans = Inf + Infi


MATLAB:

>>  besseli(0,1)

ans =
    1.2661

>>  besseli(0,10)

ans =
    2.8157e+03

>>  besseli(0,81)

ans =
    6.6864e+33

>>  besseli(0,82)

ans =
    1.8064e+34

>>  besseli(0,700)

ans =
    1.5296e+302

>>




I wrote a m-file to evaluate the function with precision for input 
parameters ultil 700, but it results too slow when I have to call the 
function several times.


-----------------------------------------------------------
function I = besseli_oct(NU, Z),

var = 1/factorial(NU);
I   = var;

for k=1:460
    var = var.*(0.25 * Z.^2)./(k*(k+NU));
    I   = I + var;
end

I = I.*( 0.5 * Z ).^NU;
-----------------------------------------------------------

The Octave's version I'm using is the 2.1.46 with ATLAS optimized 
for P4 from Paul Söderlind's Software Page, and this version doesn't 
support dynamic linking ( octave_config_info("dld")=0 ).
Have anybody any suggestion for this problem? A function written in 
C++ with the macro DEFUN_DLD_BUILTIN would work with the Octave's 
version I have?

Thanks in advance for any help.

Otavio




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