Ma's identity and its application

In the paper we distinguish the, so called, Ma's polynomials and we introduce connections of these polynomials with the classic Cauchy polynomials and the Ferrers-Jackson's polynomials. Presented connections enable to receive certain interesting divisibility relations for all these three types of polynomials and some other symmetric polynomials. Application of the discussed identities for determining the limits of quotients of the respective polynomials in two variables are also presented here.