(x-y)⁢∑k=0n(2⁢k+1)⁢Pk⁡(x)⁢Pk⁡(y)=(n+1)⁢(Pn+1⁡(x)⁢Pn⁡(y)-Pn⁡(x)⁢Pn+1⁡(y)),