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).
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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.
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© 2016 Springer International Publishing Switzerland
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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
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DOI: https://doi.org/10.1007/978-3-319-41345-7_1
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