Georgia Institute of Technology College of Sciences

In this talk we discuss some nonlinear transformations between moment sequences. One of these transformations is the following: if (a_n)_n is a non-vanishing Hausdorff moment sequence then the sequence defined by 1/(a_0 ... a_n) is a Stieltjes moment sequence. Our approach is constructive and use Euler's idea of developing q-infinite products in power series. Some others transformations will be considered as well as some relevant moment sequences and analytic functions related to them. We will also propose some conjectures about moment transformations defined by means of continuous fractions.