Optimization and Control Theory Department: 2017-03-07 Nonlinear Seminar

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> **Formal power series (Part 1)**
> At the seminar we will discuss the following statement of M. Artin:
> Let $$f(x,y)=0$$ be analytic equation ($$f$$ is analytic). We will show that if the equation has a solution $$y(x)$$ in the space of formal series than it has also analytic solution which differs from $$ y(x) $$ coefficients with large powers.

Michał Goliński
Formal power series (Part 1)

At the seminar we will discuss the following statement of M. Artin:
Let $f(x,y)=0$ be analytic equation ( $f$ is analytic). We will show that if the equation has a solution $y(x)$ in the space of formal series than it has also analytic solution which differs from $y(x)$ coefficients with large powers.