Algebraic Independence of Certain Generalized Mahler Type Numbers

In this paper the generalized Mahler type number M h (g; A, T) is defined, and in the case of multiplicatively dependent parameters gi, hi(1 . i . s) the algebraic independence of the numbers Mhi(gi;A,T)(1.i.s) is proved, where A and T are certain infinite sequences of non.negative integers and of positive integers, respectively. Furthermore, the algebraic independence result on values of a certain function connected with the generalized Mahler type number and its derivatives at algebraic numbers is also given.