February 26 2008   7:40:34.005 PM
 
CHEBYSHEV1_RULE
  FORTRAN90 version
 
  Compute a Gauss-Chebyshev type 1 rule for
 
    Integral ( -1 <= x <= +1 ) f(x) / sqrt ( 1 - x^2 ) dx
 
  of order ORDER.
 
  The user specifies ORDER and OUTPUT.
 
  OUTPUT is:
 
  "C++" for printed C++ output;
  "F77" for printed Fortran77 output;
  "F90" for printed Fortran90 output;
  "MAT" for printed MATLAB output;
 
  or:
 
  "filename" to generate 3 files:
 
    filename_w.txt - the weight file
    filename_x.txt - the abscissa file.
    filename_r.txt - the region file.
 
  The requested order of the rule is        8
 
  OUTPUT option = "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Chebyshev type 1 quadrature rule
%  ORDER =        8
%
%  Standard rule:
%    Integral ( -1 <= x <= +1 ) f(x) / sqrt ( 1 - x^2 ) dx
%    is to be approximated by
%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
    w( 1) =   0.3926990816987241    ;
    w( 2) =   0.3926990816987241    ;
    w( 3) =   0.3926990816987241    ;
    w( 4) =   0.3926990816987241    ;
    w( 5) =   0.3926990816987241    ;
    w( 6) =   0.3926990816987241    ;
    w( 7) =   0.3926990816987241    ;
    w( 8) =   0.3926990816987241    ;
 
    x( 1) =  -0.9807852804032304    ;
    x( 2) =  -0.8314696123025453    ;
    x( 3) =  -0.5555702330196020    ;
    x( 4) =  -0.1950903220161282    ;
    x( 5) =   0.1950903220161283    ;
    x( 6) =   0.5555702330196023    ;
    x( 7) =   0.8314696123025452    ;
    x( 8) =   0.9807852804032304    ;
 
  r( 1) =  -1.0000000000000000    ;
  r( 2) =   1.0000000000000000    ;
 
CHEBYSHEV1_RULE:
  Normal end of execution.
 
February 26 2008   7:40:34.010 PM