Abstract: | The Hankel determinants of the convolution powers of Catalan numbers were considered by Cigler and Krattenthaler. We evaluate these determinants for by finding shifted periodic continued fractions, which arose in application of Sulanke and Xin’s continued fraction method. These include some of the conjectures of Cigler as special cases. We also conjecture a polynomial characterization of these determinants. The same technique is used to evaluate the Hankel determinants . Similar results are obtained. |