Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In complex analysis, the term Picard theorem (named after Charles Émile Picard) refers to either of two distinct yet related theorems, both of which pertain to the range of an analytic function. The first theorem, also referred to as "Little Picard", states that if a complex functi ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In complex analysis, the term Picard theorem (named after Charles Émile Picard) refers to either of two distinct yet related theorems, both of which pertain to the range of an analytic function. The first theorem, also referred to as "Little Picard", states that if a complex function f(z) is entire and non-constant, then the set of values that f(z) assumes is either the whole complex plane or the plane minus a single point. This theorem was proved by Picard in 1879. It is a significant strengthening of Liouville's theorem which states that the image of an entire non-constant function must be unbounded.