;+
; NAME:
;   LEGCHEB
;
; AUTHOR:
;   Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
;   craigm@lheamail.gsfc.nasa.gov
;   UPDATED VERSIONs can be found on my WEB PAGE: 
;      http://cow.physics.wisc.edu/~craigm/idl/idl.html
;
; PURPOSE:
;   Compute Legendre polynomial coefficents from Chebyshev coefficients
;
; MAJOR TOPICS:
;   Curve and Surface Fitting, Special Functions
;
; CALLING SEQUENCE:
;   b = LEGCHEB(a)
;
; DESCRIPTION:
;
;   This routine computes the coefficients of a Legendre polynomial
;   expansion when the Chebyshev expansion is known.
;
;   Users can determine the Chebyshev expansion coefficients using a
;   routine like CHEBFIT, CHEBCOEF or CHEBGRID.  Then, if the Legendre
;   expansion is needed instead, this conversion routine should be
;   used.  Evaluation of the Legendre series can be performed using
;   the POLYLEG function in the IDL Astronomy Library.
;
;   Internally, the computational precision is double precision.
;   This routine relies upon the algorithm of Piessens (1974).
;
; INPUTS:
;
;   A - a vector, the coefficients of the Chebyshev series of the
;       desired function.
;
; RETURNS:
;
;   The vector B, which contains the coefficients of the Legendre
;   polynomial expansion.  Both A and B will have the same number of
;   elements and data type.
;
; KEYWORD PARAMETERS:
;
;   NONE
;
; EXAMPLE:
;
;   ;; Compute the Chebyshev series coefficients of 1/(2-X) on [-1,1]
;   A = CHEBCOEF('1d/(2d - X)', /expr)
;
;   ;; Convert to Legendre series coefficients
;   B = LEGCHEB(A)
;
; REFERENCES:
;
;   Abramowitz, M. & Stegun, I., 1965, *Handbook of Mathematical
;     Functions*, 1965, U.S. Government Printing Office, Washington,
;     D.C. (Applied Mathematical Series 55)
;   Piessens, R. 1974, Comm. ACM, v. 17, p. 25 (TOMS 473)
;
; MODIFICATION HISTORY:
;   Written and documented, CM, 25 Sep 2002
;
;  $Id: legcheb.pro,v 1.1 2002/09/25 21:12:35 craigm Exp $
;
;-
; Copyright (C) 2002, Craig Markwardt
; This software is provided as is without any warranty whatsoever.
; Permission to use, copy, modify, and distribute modified or
; unmodified copies is granted, provided this copyright and disclaimer
; are included unchanged.
;-