Sách The Abel-type polynomial identities ∗

where x, y and z are real numbers. Then the identity is called Abel identity. When we
set z = 0 in Eq.(1), it becomes the binomial identity. There are many applications of the
Abel identity [1]. And many authors offered different proofs of this identity, including the
All the identities above are dealt with a single summation. In this paper we present
three polynomial identities, which are called the Abel-type identities involving double
summations. We show the identities here first and then give their proofs in the third
Section.