Am Freitag, den 21.10.2011, 15:51 -0700 schrieb Edwin Woollett:
> On Oct. 21, 2011, I wrote about bessel_i integrate
> sign error. Using the same session, here is an
> apparent sign error when using integrate
> with bessel_y(2,x) . (The reasoning is the same.)
>
> first the 'height' (the 'base' is unity):
>
> (%i23) f(bessel_y(2,4));
> (%o23) 0.21590359460361
>
> (%i24) integrate (bessel_y(2,y),y,3.5,4.5);
> (%o24) (46650016*%pi-292890325)/445824550-(6893566*%pi-5764575)/63526475
> (%i25) f(%);
> (%o25) -0.57840103823513
>
> So both sign and magnitude error apparently.
I have done a correction of the implementation of the integral for
bessel_y. The summation indices of the formula are not correct.
Now I get:
(%i1) integrate(bessel_y(2,x),x);
(%o1) %pi*(struve_h(0,x)*bessel_y(1,x)+struve_h(-1,x)*bessel_y(0,x))*x/2
-2*bessel_y(1,x)
(%i2) integrate(bessel_y(2,x),x,3.5,4.5), numer;
(%o2) .2062014754631974
I have checked more integrals for an order n=0,1,2,3,4,5 and the
formulas now appear to be correct.
Dieter Kaiser