Bessel Function of the First Kind

[roadrunner]

Nice program!

Here's a modification that's good for non integer values of order as well:

Code:


#cas
J_n(n,x):=
BEGIN
 LOCAL b, t;
 b:=(1/π)*int(cos(n*t-x*sin(t)),t,0,π);
 IF TYPE(n)≠1 THEN
  b:=b-(sin(n*π)/π)*int(e^(-x*sinh(t)-n*t),t,0,∞);
 END;
 RETURN approx(b);
END;
#end

And a cool chart for n= -1, -0.5, 0, 0.5, and 1 that only took a few minutes to draw on the prime:

   

-road