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



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.

Ray