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Simple integral over special functions---HOW?

• To: mathgroup@smc.vnet.net
• Subject: [mg12565] Simple integral over special functions---HOW?
• From: "Michael A. Morrison" <morrison@phyast.nhn.ou.edu>
• Date: Sat, 23 May 1998 18:11:25 -0400
• Organization: University of Oklahoma

Hi. I have repeatedly run into trouble trying to get Mathematica to
evaluate analytically simple integrals involving special functions. For
example, the following integral has a simple analytic form:
        Integrate[LegendreP[n,x]/Sqrt[1-x^2],{x,-1,+1}] When I enter the
above into Mathematica, it returns the integral unevaluated unless I
specify a value for n. Figuring that the problem was that Mathematica
didn't realize that n is a non-negative integer, I did the following:
        n/: IntegerQ[n] = True;
        Integrate[LegendreP[n,x]/Sqrt[1-x^2], {x,-1,+1}, Assumptions ->
n  >=  0]
Again, Mathematica returned the integral unevaluated, along with the
assumption.
It's as though the information that n is an integer in the Global`
context doesn't get communicated to the Integrate command. Can anyone
tell me (a) whether the above method fully specifies n as an integer in
all such situations (I have other failures where function definitions
seem unaware of such a specification) and if not, how to properly
specify a symbol as an integer and (b) how to make Integrate evaluate
integrals such as the example above?
Many thanks for considering this question. --
Michael A. Morrison
Dept. Physics & Astronomy
University of Oklahoma
Norman, OK 73019
Phone: 405 325-3961
FAX: 405 325-7557
EMAIL: morrison@mail.nhn.ou.edu
WEB PAGE: http://www.nhn.ou.edu/~morrison

• Follow-Ups:
  • Re: Simple integral over special functions---HOW?
    • From: Sean Ross <seanross@worldnet.att.net>