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Institut für Astronomie und AstrophysikAbteilung AstronomieSand 1, D-72076 Tübingen, GermanyNew Address! -- Neue Adresse! |
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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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