[Maxima-bugs] [ maxima-Bugs-2862208 ] specint(exp(-s*t)*t^n*bessel_j(1, t), t) is wrong
Subject: [Maxima-bugs] [ maxima-Bugs-2862208 ] specint(exp(-s*t)*t^n*bessel_j(1, t), t) is wrong
From: Raymond Toy
Date: Mon, 21 Sep 2009 12:50:11 -0400
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