Name

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        FLEGENDRE

Purpose

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      Compute the first M terms in a Legendre polynomial expansion.

Explanation

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      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

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      result = FLEGENDRE( X, M)

Inputs

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

Outputs

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      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

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      (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

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      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

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