SLATEC Routines --- QCHEB ---

```*DECK QCHEB
SUBROUTINE QCHEB (X, FVAL, CHEB12, CHEB24)
C***BEGIN PROLOGUE  QCHEB
C***SUBSIDIARY
C***PURPOSE  This routine computes the CHEBYSHEV series expansion
C            of degrees 12 and 24 of a function using A
C            FAST FOURIER TRANSFORM METHOD
C            F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
C            F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
C            Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (QCHEB-S, DQCHEB-D)
C***KEYWORDS  CHEBYSHEV SERIES EXPANSION, FAST FOURIER TRANSFORM
C***AUTHOR  Piessens, Robert
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C           de Doncker, Elise
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C***DESCRIPTION
C
C        Chebyshev Series Expansion
C        Standard Fortran Subroutine
C        Real version
C
C        PARAMETERS
C          ON ENTRY
C           X      - Real
C                    Vector of dimension 11 containing the
C                    Values COS(K*PI/24), K = 1, ..., 11
C
C           FVAL   - Real
C                    Vector of dimension 25 containing the
C                    function values at the points
C                    (B+A+(B-A)*COS(K*PI/24))/2, K = 0, ...,24,
C                    where (A,B) is the approximation interval.
C                    FVAL(1) and FVAL(25) are divided by two
C                    (these values are destroyed at output).
C
C          ON RETURN
C           CHEB12 - Real
C                    Vector of dimension 13 containing the
C                    CHEBYSHEV coefficients for degree 12
C
C           CHEB24 - Real
C                    Vector of dimension 25 containing the
C                    CHEBYSHEV Coefficients for degree 24
C