Hypergeometric functions for function fields and transcendence
Dinesh S. Thakur, Zhi‐Ying Wen, Jia-Yan Yao, Liang Zhao · Comptes Rendus Mathématique · 2009
We study hypergeometric functions for F q [ T ] , and show in the entire (non-polynomial) case the transcendence of their special values at nonzero algebraic arguments which generate extension of the rational function field with less than q places at infinity. We also characterize in the balanced case the algebraicity of hypergeometric functions.