Abstract
Our main goal in this chapter is to give an elementary proof of Picard’s first and second theorems, which we base upon Schottky’s theorem (Theorem 1.2).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Throughout these notes, a function f(z) of a complex variable z is said to be regular at a point \(z_*\in {\mathbb C}\) if it is holomorphic (i.e., satisfies the Cauchy–Riemann equations) in an open neighbourhood of \(z_*\). The function f(z) is regular in a set \(S\subset {\mathbb C}\) if it is regular at every point of S.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Viola, C. (2016). Picard’s Theorems. In: An Introduction to Special Functions. UNITEXT(), vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-41345-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-41345-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41344-0
Online ISBN: 978-3-319-41345-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)