Legendre polynomials

Hello,
I would like to do some computations with Legendre polynomials. I would like to know, if Maple is able to do some simplifications and use orthogonality of Legendre polynomials.

For example

> Int(LegendreP(m,x)*LegendreP(n, x), x=-1..1);

This integral should be zero or 2/(2*n+1), depending on the relation between m and n.

Is there any chance to get it (maybe using the procedure assume() )?

another example:

> diff(LegendreP(n,x), x$n);
This should be (2*n)!

Thank you very much for your help.

Karel Srot

alec's picture

Product Suggestions forum

That should be, probably, put in the Product Suggestion forum. From other point of view, it doesn't seem very active. My posts there didn't get any responses.

__________
Alec Mihailovs
http://mihailovs.com/Alec/

I hope extremly maple can

I hope extremly maple can manipulate these kind things

JacquesC's picture

Good luck

The maple philosophy has long been that generic answers are sufficient. In fact, that completely correct answer, with all the cases spelled out, is too much for most users. In other words, most users can't handle the truth.

To be fair, that has been changing slowly. In 1991-1992, the prevailing philosophy was that the dreaded square root bug could never be eradicated, and yet in 1993 it was mostly gone and Maple [and all other Computer Algebra Systems] survived. Then it was various automatic simplifications that were supposed to be impossible to fix - and in Maple 6,7,8, a lot of them were removed and Maple 10's computational power is just fine. And so it is for fixing various other parts of Maple to output correct answers instead of generic answers. From what I can see, steady progress is being made on this front too, but the pace is not what one would call quick.

From my experience with the typical pace of development on these things (I have been using Maple since 1985, and used to be at Maplesoft before I heard the call of academia a few years ago), either there will be a release soon (2008?) where huge progress is made, or most of these problems will have been fixed by slow evolution by roughly 2011. And yes, I am serious about those timescales.

Steady pressure from users does make a difference. Actually, pressure from reviewers in trade magazines is even more effective! If you want to get Maplesoft to change something quickly, put it in print in a trade magazine with a high circulation, and where the blogosphere picks it up.

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