integrate of bessel_i sign error?

• Subject: integrate of bessel_i sign error?
• From: Edwin Woollett
• Date: Sat, 22 Oct 2011 13:39:12 -0700

On Oct.22, 2011, Dieter Kaiser  wrote:



>With a corrected formula for the integral of bessel_i(1,x) in Maxima I
>get:
>
>(%i2) integrate(bessel_i(1,%i*x),x,1,2);
>(%o2) %i*bessel_i(0,%i)-%i*bessel_i(0,2*%i)
>(%i3) %,numer;
>(%o3) .5413069074167309*%i
>
>The result is equivalent to
>
>(%i4) %i*(bessel_j(0,1) - bessel_j(0,2)), numer;
>(%o5) .5413069074167309*%i
>
>This is valid, because bessel_i(n,%i*x) = %i^n*bessel_j(n,x) for n an
>integer. Perhaps we should implement the this identity.

Yes, that would be nice.

Thanks for looking at this.

Ted

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