Am Freitag, den 21.10.2011, 14:33 -0700 schrieb Edwin Woollett:
> integrate doesn't seem to give a correct value
> for the integral of bessel_i, based on numerical
> values Maxima uses.
>
> For a small integration range and a smooth
> function, a rough value of the integral
> is base*height. Here we use a base = 1
> integrating from y = 1 to y = 2,
> and use a height the value
> half way across the range:
>
> (%i1) load(nint);
> (%o1) "c:/work2/nint.mac"
> (%i2) ratprint:false$
> (%i3) f(a):= fchop(expand(float(a)))$
>
> here is the height:
>
> (%i4) f(bessel_i(1,%i*1.5));
> (%o4) 0.5579365079101*%i
>
> here is the integral over a range = 1:
>
> (%i5) f(integrate(bessel_i(1,%i*y),y,1,2));
> (%o5) -0.54130690741673*%i
>
> integrate appears to produce the wrong sign
> for this integral??
Yes, I think the integral of bessel_i(0,x) is wrong:
(%i1) integrate(bessel_i(1,x),x);
(%o1) - (bessel_i(0, x))
The correct answer should be bessel_i(0,x), see e. g.
http://functions.wolfram.com/Bessel-TypeFunctions/BesselI/21/01/01/
I will correct it.
Dieter Kaiser