From these definitions, it can be shown that the above scalar product can be expanded as I ( 1 ) ⋅ ⋅ J ( 1 ) = ∑ ∑ n = − − 1 + 1 ( − − 1 ) n I n ( 1 ) J − − n ( 1 ) = I 0 ( 1 ) J 0 ( 1 ) − − I − − 1 ( 1 ) J + 1 ( 1 ) − − I + 1 ( 1 ) J − − 1 ( 1 ) .