Name

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      POLYLEG

Purpose

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      Evaluate a Legendre polynomial with specified coefficients.

Explanation

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      Meant to be used analogously to the POLY function in the IDL User's
      Library distribution.

Calling Sequence

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      Result = POLYLEG( X, C )

Inputs

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      X - input variable, scalar or vector
      C - vector of Legendre polynomial coefficients.

Outputs

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      POLYLEG returns a result equal to:
              C[0] + C[1]*P_1(x) + C[2]*P_2(x) + ...
      where P_j(x) is the jth Legendre polynomial. The output will have
      the same dimensions as the input X variable.

Example

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      If x = [0.5, 1.0] and C = [2.4, 1.3, 2.5] then
      print, polyleg(x, c) ====> [2.7375, 6.20]
      The result can be checked using the first 3 Legendre polynomial terms
      C[0] + C[1]*x + C[2]*(0.5*(3*x^2-1))

Method

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      Uses the recurrence relation of Legendre polynomials
              (n+1)*P_n+1(x) = (2n+1)*x*P_n(x) - n*P_n-1(x)
      evaluated with the Clenshaw recurrence formula, see Numerical Recipes
      by Press et al. (1992), Section 5.5

Revision History

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      Written W. Landsman Hughes STX Co. April, 1995
      Fixed for double precision W. Landsman May, 1997
      Converted to IDL V5.0 W. Landsman September 1997