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FLEGENDRE

FLEGENDRE

Name


        FLEGENDRE

Purpose


      Compute the first M terms in a Legendre polynomial expansion.

Explanation


      Meant to be used as a supplied function to SVDFIT.
      This procedure became partially obsolete in IDL V5.0 with the
      introduction of the /LEGENDRE keyword to SVDFIT and the associated
      SVDLEG function. However, note that, unlike SVDLEG, FLEGENDRE works
      on vector values of X.

Calling Sequence


      result = FLEGENDRE( X, M)

Inputs


      X - the value of the independent variable, scalar or vector
      M - number of term of the Legendre expansion to compute, integer scalar

Outputs


      result - (N,M) array, where N is the number of elements in X and M
              is the order. Contains the value of each Legendre term for
              each value of X

Example


      (1) If x = 2.88 and M = 3 then
      IDL> print, flegendre(x,3) ==> [1.00, 2.88, 11.9416]
      This result can be checked by explicitly computing the first 3 Legendre
      terms, 1.0, x, 0.5*( 3*x^2 -1)
      (2) Find the coefficients to an M term Legendre polynomial that gives
              the best least-squares fit to a dataset (x,y)
              IDL> coeff = SVDFIT( x,y,M,func='flegendre')
     
          The coefficients can then be supplied to the function POLYLEG to
              compute the best YFIT values for any X.

Method


      The recurrence relation for the Legendre polynomials is used to compute
      each term. Compare with the function FLEG in "Numerical Recipes"
      by Press et al. (1992), p. 674

Revision History


      Written Wayne Landsman Hughes STX April 1995
      Converted to IDL V5.0 W. Landsman September 1997



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