Commutation Symbols   6J

Assuming that x> y, we define

Dxy =vxlxly

and   Nxy = Dx+1 : y+i +Dx+2 :y+2 +

so that   axy =    .

DxY

Also   Axy = — [vdxy +v'dx+1 :y+l + ... ].

1xy Assuming that x> y, we define

x+1

Cxy=T   dxY=vx+1 SXY—1x+1:Y+1)

and   Mx, = Cxy +Cx+i : y+i + .. .

so that   ~1x'

xy =

DxY

x+y

The student should try the result of making DxY=v 2 .lx.ly. 13. We have A x =   `c¢xµx+cdt

0

`mac

lx fvlx+x+dt

J   DDx+t l ~x+Edt. 0

and   11'1x=Cx+Cx+i+Cx+2+ ... =J Dx+ttlx+tdt 0

so that   Ax =   x .

Dx

f For practical work, since,   =   Dx+flax+tdt,

0

we take   Cx = 1 XDx+iux+3, approximately

_   J We write   = Dx+tl-tx+tdt

0