bessel_y sign error with integrate?



On Oct. 22, 2011, Dieter Kaiser  wrote:

>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.

Thanks again for looking at these bugs.

I looked at Wolfram Alpha's symbolic answer for

  Integrate[BesselY[2,x],{x,a,b}]

and tried it out in Maxima, where it gave the wrong sign
but the right magnitude.

This is curious, because their answer to

    NIntegrate[BesselY[2,y],{y,3.5,4.5}]

  *does* give both the right sign and magnitude.

Ted