# [Maxima] [Maxima-bugs] [ maxima-Bugs-2862208 ] specint(exp(-s*t)*t^n*bessel_j(1, t), t) is wrong

Dieter Kaiser drdieterkaiser at web.de
Mon Sep 21 15:47:21 CDT 2009

```Am Montag, den 21.09.2009, 12:50 -0400 schrieb Raymond Toy:
> SourceForge.net wrote:
> > In the routine lgf24 in hyp.lisp the first parameter of the Associated Legendre Polynom is wrongly calculated. We have
> >
> >    (n (mul -1 (add a a m))) ; that is not 2*a-c
> >
> > The correct calculation would be
> >
> >    (n (sub (add a a) c)) ; calculate 2*a-c
> >
> >
> Based on the comments before legf24:
>
> ;; Let a = -n/2-m/2, b = 1/2-n/2-m/2, c = 1-m.  Then m = 1-c.  Again,
> ;; we have 2 possible (equivalent) values for n:
> ;;
> ;; n = -(2*a + 1 - c) or n = c-2*b
> ;;
> ;; The code below chooses the first solution.
>
> Is the calculation of n = -(2*a+1-c) incorrect?
>
> If not then the expression
>
> (n (mul -1 (add a a m)))
>
> is computing n = -(2*a+1-c) = -(2*a+m) since 1-c=m.
>
> >From this I conclude that you think the formula given there is wrong.  I
> don't have a copy of the table of integral transforms with me right now
> so I can't tell if the formula was transcribed incorrectly or not.

Yes, I think the formulas above the code are not correct, but the
formula A&S 5.4.11 in the code is correct. Furthermore, I had a look at
wolfram alpha to check the result for hypergeometric(a,a+1/2,c,x).

The Laplace transform of t^n*bessel_y(v,a*t) is a test of the routine
legf24. I think there are no more examples which check this routine.
After the correction the Laplace transform is correct.

Dieter Kaiser

```