'****************************************************
'*   Program to demonstrate Chebyser subroutine     *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* by F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 2   *
'*    A( 0) = -1                                    *
'*    A( 1) = 0                                     *
'*    A( 2) = 2                                     *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 3   *
'*    A( 0) = 0                                     *
'*    A( 1) = -3                                    *
'*    A( 2) = 0                                     *
'*    A( 3) = 4                                     *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 4   *
'*    A( 0) = 1                                     *
'*    A( 1) = 0                                     *
'*    A( 2) = -8                                    *
'*    A( 3) = 0                                     *
'*    A( 4) = 8                                     *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 5   *
'*    A( 0) = 0                                     *
'*    A( 1) = 5                                     *
'*    A( 2) = 0                                     *
'*    A( 3) = -20                                   *
'*    A( 4) = 0                                     *
'*    A( 5) = 16                                    *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 6   *
'*    A( 0) = -1                                    *
'*    A( 1) = 0                                     *
'*    A( 2) = 18                                    *
'*    A( 3) = 0                                     *
'*    A( 4) = -48                                   *
'*    A( 5) = 0                                     *
'*    A( 6) = 32                                    *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 7   *
'*    A( 0) = 0                                     *
'*    A( 1) = -7                                    *
'*    A( 2) = 0                                     *
'*    A( 3) = 56                                    *
'*    A( 4) = 0                                     *
'*    A( 5) = -112                                  *
'*    A( 6) = 0                                     *
'*    A( 7) = 64                                    *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 8   *
'*    A( 0) = 1                                     *
'*    A( 1) = 0                                     *
'*    A( 2) = -32                                   *
'*    A( 3) = 0                                     *
'*    A( 4) = 160                                   *
'*    A( 5) = 0                                     *
'*    A( 6) = -256                                  *
'*    A( 7) = 0                                     *
'*    A( 8) = 128                                   *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 9   *
'*    A( 0) = 0                                     *
'*    A( 1) = 9                                     *
'*    A( 2) = 0                                     *
'*    A( 3) = -120                                  *
'*    A( 4) = 0                                     *
'*    A( 5) = 432                                   *
'*    A( 6) = 0                                     *
'*    A( 7) = -576                                  *
'*    A( 8) = 0                                     *
'*    A( 9) = 256                                   *
'*                                                  *
'* Chebyshev polynomial coefficients for degree 10  *
'*    A( 0) = -1                                    *
'*    A( 1) = 0                                     *
'*    A( 2) = 50                                    *
'*    A( 3) = 0                                     *
'*    A( 4) = -400                                  *
'*    A( 5) = 0                                     *
'*    A( 6) = 1120                                  *
'*    A( 7) = 0                                     *
'*    A( 8) = -1280                                 *
'*    A( 9) = 0                                     *
'*    A( 10) = 512                                  *
'*                                                  *
'****************************************************
DEFINT I-N
DEFDBL A-H, O-Z
CLS
PRINT
DIM B(10, 10)
FOR n = 2 TO 10
  GOSUB 1000
  PRINT " Chebyshev polynomial coefficients for degree "; n
  PRINT
  FOR i = 0 TO n
    PRINT "  A("; i; ") = "; B(n, i)
  NEXT i
  PRINT : IF n < 10 THEN INPUT A$
NEXT n
PRINT
END

'********************************************************
'* Chebyshev series coefficients evaluation subroutine  *
'* ---------------------------------------------------- *
'* The order of the polynomial is n. The coefficients   *
'* are returned in the array B(i,j), i is the degree of *
'* the polynomial, j is the coefficient order.          *
'********************************************************
1000 'Establish t0 and t1 coefficients
  B(0, 0) = 1: B(1, 0) = 0: B(1, 1) = 1
  'Return if order is less than two
  IF n < 2 THEN RETURN
  FOR i = 2 TO n
    FOR j = 1 TO i
      'Basic recursion relation
      B(i, j) = 2 * B(i - 1, j - 1) - B(i - 2, j)
    NEXT j
    B(i, 0) = -B(i - 2, 0)
  NEXT i
RETURN

'End of file Chebyser.bas