function [alf, bet] = alfbet(n,x,a,b)
if (n==1)
  alf = F([0 x]);
  bet = F([1 x]);
else
  [alf0x, bet0x] = alfbet(n-1,[0 x],a,b);
  [alf1x, bet1x] = alfbet(n-1,[1 x],a,b);
  alf =    a  * alf0x -    b  * bet0x;
  bet = (a-1) * alf1x - (b-1) * bet1x;
end
return



function [alf, bet] = alfbet_old(n,x,a,b)
%if (n==2)
%  alf =  a   *F([1 1 x]) - b   *F([2 1 x]);
%  bet = (a-1)*F([1 2 x]) -(b-1)*F([2 2 x]);
if (n==1)
  alf = F([1 x]);
  bet = F([2 x]);
else
  [alf0x, bet0x] = alfbet(n-1,[1 x],a,b);
  [alf1x, bet1x] = alfbet(n-1,[2 x],a,b);
  alf =    a  * alf0x -    b  * bet0x;
  bet = (a-1) * alf1x - (b-1) * bet1x;
end
return