Multiplication laws for differential equations

With V. Golyshev. This talk is an overview of how some cases of Langlands' correspondence for function fields can be interpreted very classically and explicitly. In particular, we see how formulas of Clausen's type and multiplication identities for Bessel functions arise this way. For example, our approach gives an explicit correspondence between solutions of the Dwork's accessory parameter problem as studied by Beukers, and automorphic forms.