Name

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  LEGCHEB

Author

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  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

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  Compute Legendre polynomial coefficents from Chebyshev coefficients

Major Topics

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  Curve and Surface Fitting, Special Functions

Calling Sequence

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  b = LEGCHEB(a)

Description

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  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

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  A - a vector, the coefficients of the Chebyshev series of the
      desired function.

Returns

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  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

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  NONE

Example

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  ;; 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

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  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

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  Written and documented, CM, 25 Sep 2002