Advanced determinant calculus: A complement

This is a complement to my previous article “Advanced Determinant Calculus” [C. Krattenthaler, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 (1999) (“The Andrews Festschrift”), Article B42q, 67 pp.]. In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory [G. Almkvist, C. Krattenthaler, J. Petersson, Some new formulas for π, Experiment. Math. 12 (2003) 441-456]. Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.