Integrability and geometry of the Wynn recurrence

We show that the Wynn recurrence (the missing identity of Frobenius Padé approximation theory) can be incorporated into theory integrable systems as a reduction discrete Schwarzian Kadomtsev–Petviashvili equation. This allows, in particular, to present geometric meaning construction appropriately constrained quadrangular set points. The interpretation is valid for projective line over arbitrary skew field what motivates consider non-commutative theory. transfer corresponding elements, including identities, level using quasideterminants. Using an example characteristic series Fibonacci language we application regular languages. introduce version discrete-time Toda lattice equations together with their integrability structure. Finally, discuss different context analytic functions.