Institut für Astronomie und AstrophysikAbteilung AstronomieSand 1, D-72076 Tübingen, GermanyNew Address! -- Neue Adresse! |
POLYLEG
Evaluate a Legendre polynomial with specified coefficients.
Meant to be used analogously to the POLY function in the IDL User's Library distribution.
Result = POLYLEG( X, C )
X - input variable, scalar or vector C - vector of Legendre polynomial coefficients.
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.
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))
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
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
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