From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Gauss-Lobatto-Legendre quadrature point
Date: 9 Jul 2001 14:12:55 GMT
Newsgroups: sci.math.num-analysis
Summary: Finding positions of nodes for numerical integration

In article <3B45C412.DDAD3164@imtek.uni-freiburg.de>,
 Liu Zhenyu <zhenyu@imtek.uni-freiburg.de> writes:
|> Hello :
|> 
|>   Is there anyone know the point position and the weighed coefficient of
|> Gauss-Lobatto-Legendre quadrature in the interval [-1,1], which N from
|> 1~5 .
|> 

1)Engels: numerical quadrature and cubature,
acad. press. 
 has it for n even on page 327

2)following Engels, Stroud "approximate calculation of multiple integrals",
prentice hall, should have it, 
but it has been stolen from our library, hence I cannot check it.

3)maybe you let 
http;//www.netlib.org/toms/655 or /726 do the job for you.
and finally:

4)the nodes are the zeroes of (1-x^2)*P_{n-1}'(x), P_i the ordinary
Legendre polynomial and the weights are the integrals of the associated 
Lagrange-polynomials, as usual.

hope that helps
peter