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Path: utzoo!watmath!clyde!cbosgd!ihnp4!drutx!drux2!ljc
From: ljc@drux2.UUCP (ClerLJ)
Newsgroups: net.math,net.physics
Subject: value of an integral
Message-ID: <823@drux2.UUCP>
Date: Thu, 20-Feb-86 11:30:30 EST
Article-I.D.: drux2.823
Posted: Thu Feb 20 11:30:30 1986
Date-Received: Fri, 21-Feb-86 06:20:07 EST
Organization: AT&T Information Systems Laboratories, Denver
Lines: 52
Xref: watmath net.math:2866 net.physics:3876



Can someone out "there" show me an elementary (but, perhaps
involving "tricks") method for integrating the following
function:

int from 0 to inf s sup 3 over {e sup s - 1} ds

or "written" out:

      ( oo
      |        3
      |       s
      | -------------- ds
      |     s
      |    e  -  1
      ) 0

By elementary, I mean you can't use the fact that the integral
is related to both the Gamma Function and the Riemann Zeta Func-
tion or use techniques from the theory of complex variables.
Essentially, using only techniques from the standard undergraduate
calculus sequence, find the value of the integral.

However, techniques as used to find the value of:

int from 0 to inf e sup x sup 2 dx

are acceptable.

The value of the integral, if my memory has not failed me, is pi^2/15.

This integral results when considering the radiated power of a black
body, integrated over all wavelengths.  Hence, the cross posting to
net.physics.

Note to net.math readers (if it applies to you read it, otherwise
no offense intended!):

I know I'm in for some scathing remarks that this is not mathematics,
(high school algebra: yes, calculus: maybe) in that there is no group
theory, no topology, and no set theory involved.  Well, those of us
in applied mathematics are already tired of comments of that sort,
so please don't bother :-).

Maybe what is needed is net.math.appld, and our pure mathematics
brethren wouldn't have to read such (from their perspective)
tom-foolery as this article.

Thanx in advance!
				larry cler
				ihnp4!drux2!ljc