\[(x-y)\sum_{k=0}^{n}(2k+1)P_{k}\left(x\right)Q_{k}\left(y\right)=(n+1)\left(P_{%
n+1}\left(x\right)Q_{n}\left(y\right)-P_{n}\left(x\right)Q_{n+1}\left(y\right)%
\right)-1.\]