Analytical Real Functions

This lecture covers the concept of analytical real functions, focusing on the series expansion and properties of u(x). It discusses the derivation of u in DEIR, the definition of u in a neighborhood of o, and the conditions for u to satisfy Pck in a neighborhood of DER. The lecture also explores the analytical properties of u, the nullity of u's partial derivatives, and the implications for the function's behavior in different neighborhoods. Additionally, it delves into the relationship between u and its derivatives, providing insights into the behavior of u in various contexts.