Special values of fractional hypergeometric functions for function fields (Q1759774)

Hypergeometric functions over a function field were introduced by \textit{D. S. Thakur} [Finite Fields Appl. 1, No. 2, 219--231 (1995; Zbl 0838.11043)]; see also the reviewer's ``Analysis in positive characteristic.'' Cambridge: Cambridge University Press (2009; Zbl 1171.12005)]. The author characterizes algebraic functions within the above class, and shows the transcendence of special values at some nonzero algebraic arguments. For related results see also [\textit{D. S. Thakur, Z.-Y. Wen}, the author and \textit{L. Zhao}, J. Reine Angew. Math. 657, 135--171 (2011; Zbl 1227.11088)].