'****************************************************
'*   Program to demonstrate Legendre coefficients   *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'*                                                  *
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'* Legendre polynomial coefficients for order 2     *
'*                                                  *  
'* A( 0) =   -0.500000                              *
'* A( 1) =    0.000000                              *
'* A( 2) =    1.500000                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 3     *
'*                                                  *  
'* A( 0) =    0.000000                              *
'* A( 1) =   -1.500000                              *
'* A( 2) =    0.000000                              *
'* A( 3) =    2.500000                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 4     *
'*                                                  *  
'* A( 0) =    0.375000                              *
'* A( 1) =    0.000000                              *
'* A( 2) =   -3.750000                              *
'* A( 3) =    0.000000                              *
'* A( 4) =    4.375000                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 5     *
'*                                                  *  
'* A( 0) =    0.000000                              *
'* A( 1) =    1.875000                              *
'* A( 2) =    0.000000                              *
'* A( 3) =   -8.750000                              *
'* A( 4) =    0.000000                              *
'* A( 5) =    7.875000                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 6     *
'*                                                  *  
'* A( 0) =   -0.312500                              *
'* A( 1) =    0.000000                              *
'* A( 2) =    6.562500                              *
'* A( 3) =    0.000000                              *
'* A( 4) =  -19.687500                              *
'* A( 5) =    0.000000                              *
'* A( 6) =   14.437500                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 7     *
'*                                                  *  
'* A( 0) =    0.000000                              *
'* A( 1) =   -2.187500                              *
'* A( 2) =    0.000000                              *
'* A( 3) =   19.687500                              *
'* A( 4) =    0.000000                              *
'* A( 5) =  -43.312500                              *
'* A( 6) =    0.000000                              *
'* A( 7) =   26.812500                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 8     *
'*                                                  *  
'* A( 0) =    0.273438                              *
'* A( 1) =    0.000000                              *
'* A( 2) =   -9.843750                              *
'* A( 3) =    0.000000                              *
'* A( 4) =   54.140625                              *
'* A( 5) =    0.000000                              *
'* A( 6) =  -93.843750                              *
'* A( 7) =    0.000000                              *
'* A( 8) =   50.273438                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 9     *
'*                                                  *  
'* A( 0) =    0.000000                              *
'* A( 1) =    2.460938                              *
'* A( 2) =    0.000000                              *
'* A( 3) =  -36.093750                              *
'* A( 4) =    0.000000                              *
'* A( 5) =  140.765625                              *
'* A( 6) =    0.000000                              *
'* A( 7) = -201.093750                              *
'* A( 8) =    0.000000                              *
'* A( 9) =   94.960938                              *
'*                                                  *  
'* <Enter> to continue...                           *
'*                                                  *  
'* Legendre polynomial coefficients for order 10    * 
'*                                                  *  
'* A( 0) =   -0.246094                              *
'* A( 1) =    0.000000                              *
'* A( 2) =   13.535156                              *
'* A( 3) =    0.000000                              *
'* A( 4) = -117.304688                              *
'* A( 5) =    0.000000                              *
'* A( 6) =  351.914063                              *
'* A( 7) =    0.000000                              *
'* A( 8) = -427.324219                              *
'* A( 9) =    0.000000                              *
'* A(10) =  180.425781                              *
'*                                                  * 
'****************************************************
defint i-n
defdbl a-h,o-z
  cls
  dim A(10),B(10,10)
  for n=2 to 10
    print
    print " Legendre polynomial coefficients for order"; n
    print
    gosub 1000
    for k=0 to n
      print using "   A(##) = ####.######"; k; A(k)
    next k
    print
    if n <> 10 then input r$
  next n
  print
end

'******************************************************
'* Legendre series coefficients evaluation subroutine *
'* by means of recursion relation. The order of the   *
'* polynomial is n. The coefficients are returned in  *
'* A(i).                                              *
'******************************************************
1000 'Establish p0 and p1 coefficients
  B(0,0)=1 : B(1,0)=0 : B(1,1)=1
  'Return if order is less then 2
  if n<2 then return
  for i=2 to n
    B(i,0)=-(i-1)*B(i-2,0)/i
    for j=1 to i
      'Basic recursion relation
      B(i,j)=(i+i-1)*B(i-1,j-1)-(i-1)*B(i-2,j)
      B(i,j)=B(i,j)/i
    next j
  next i
  for i=0 to n
    A(i)=B(n,i)
  next i
return

'End of file Legendre.bas