Expansion formulas for Apostol type Q-Appell polynomials, and their special cases

We present identities of various kinds for generalized q-ApostolBernoulli and Apostol-Euler polynomials and power sums, which resemble q-analogues of formulas from the 2009 paper by Liu and Wang. These formulas are divided into two types: formulas with only q-ApostolBernoulli, and only q-Apostol-Euler polynomials, or so-called mixed formulas, which contain polynomials of both kinds. This can be seen as a logical consequence of the fact that the q-Appell polynomials form a commutative ring. The functional equations for Ward numbers operating on the q-exponential function, as well as symmetry arguments, are essential for many of the proofs. We conclude by finding multiplication formulas for two q-Appell polynomials of general form. This brings us to the q-H polynomials, which were discussed in a previous paper