where x, y and z are real numbers. Then the identity is called Abel identity. When weset z = 0 in Eq.(1), it becomes the binomial identity. There are many applications of theAbel identity . And many authors offered different proofs of this identity, including theAll the identities above are dealt with a single summation. In this paper we presentthree polynomial identities, which are called the Abel-type identities involving doublesummations. We show the identities here first and then give their proofs in the thirdSection...