NetNews Usenet Archive 1992 #26/NN_1992_26.iso/spool/sci/math/14774

Internet Message Format | 1992-11-11 | 1.6 KB

Xref: sparky sci.math:14774 sci.math.symbolic:2947
Newsgroups: sci.math,sci.math.symbolic
Path: sparky!uunet!wri!news
From: [e-mail] (Victor Adamchik)
Subject: Re: Help wanted in integration.
Message-ID: <[e-mail]>
Sender: [e-mail]
Nntp-Posting-Host: tuamotu.wri.com
Organization: Wolfram Research, Inc.
References: <[e-mail]>
Date: Wed, 11 Nov 1992 21:14:17 GMT
Lines: 46

In article <[e-mail]> [e-mail] (John Cordes)
writes:
> To those who have followed this thread:
>
>  Sorry! I believe there is one more correction to make, for the case d=c
> only. See below.

<stuff deleted>

>  Alas, my algebra did go wrong after all. The corrected result (for the
> case d = c, a > b) is as above but without the factor 31, thus:
>
> (1/32) * Pi^2 * b / c^2  +  Pi^4 * b^2 * (a-b/3) / 8.
>
>  This evaluates to 328.981001... for a = 4, b = 3, c = 2, and so is now in
> agreement with the numerical integration.
>
>
>   John Cordes, Dept. of Physics,
>   Dalhousie University, Halifax, N.S.,
>   Canada  B3H 3J5       Internet: [e-mail]


I got the same result for d = c, a > b.
For b > a it is

(a*Pi^2*(3 - 4*a^2*c^2*Pi^2 + 12*a*b*c^2*Pi^2))/(96*c^2)

So finally we have:

for integers a,b,c and d:

1. c != d

if 0 < a <= b then (a*(c^2 + d^2)*Pi^2)/(4*(c^2 - d^2)^2)
if 0 < b <= a then (b*(c^2 + d^2)*Pi^2)/(4*(c^2 - d^2)^2)

2. c == d

if 0 < a <= b then (a*Pi^2*(3 - 4*a^2*c^2*Pi^2 + 12*a*b*c^2*Pi^2))/(96*c^2)
if 0 < b <= a then (b*Pi^2*(3 - 4*b^2*c^2*Pi^2 + 12*a*b*c^2*Pi^2))/(96*c^2)

--
Victor Adamchik
[e-mail]