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From: hoffman@hdsvx1.UUCP (Richard Hoffman)
Newsgroups: sci.physics
Subject: Re: Gauss Legendre Quadratures
Message-ID: <855@hdsvx1.UUCP>
Date: Mon, 20-Oct-86 09:43:57 EDT
Article-I.D.: hdsvx1.855
Posted: Mon Oct 20 09:43:57 1986
Date-Received: Wed, 22-Oct-86 22:55:04 EDT
References: <220@sri-arpa.ARPA>
Reply-To: hoffman@hdsvx1.UUCP (Richard hoffman)
Organization: Schlumberger HDS, Houston
Lines: 19

In article <220@sri-arpa.ARPA> anderson@nrl-csr (Paul Anderson) writes: 
>I need to obtain an approximation to a function over the range [0,x] using
>a Gauss-Legendre quadrature routine.  I can find references to tables where
>the weights are given over the interval [-1,1], but not over the interval [0,x]
>where x will be a variable real number greater than zero, but specified prior
>to the integration.

The reason you can only find them on the range [-1,1] is that any function
on any other range can be transformed into a function on the range [-1,1].
Thus, if your function is f(x) on the range [0,k], then let g(x) = k(x+1)/2,
and interpolate the function f(g(x)) on the range [-1,1].  Alternately,
you can use g(x) to transform the quadrature points into points in [0,k].
This might be more efficient if you have many functions to evaluate over the
same range.
-- 
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