In this paper we shall survey the various methods of evaluating Hankel
determinants and as an illustration we evaluate some Hankel determinants of a
q-analogue of Catalan numbers. Here we consider
(abq2;q)n​(aq;q)n​​ as a q-analogue of Catalan numbers
Cn​=n+11​(n2n​), which is known as the moments of the little
q-Jacobi polynomials. We also give several proofs of this q-analogue, in which
we use lattice paths, the orthogonal polynomials, or the basic hypergeometric
series. We also consider a q-analogue of Schr\"oder Hankel determinants, and
give a new proof of Moztkin Hankel determinants using an addition formula for
2​F1​.Comment: 17 page