Abstract
Holomorphic functions are characterized by the equation ∂É/∂z = 0. In this chapter, we shall study the equation ∂É/∂̄z = g when g has compact support. We shall obtain an explicit solution which leads to a variant of the Cauchy integral formula. This variant can often be used instead of the usual Cauchy formula, and has the advantage of not involving winding numbers. We shall illustrate this principle with a variant of the argument principle and a proof of the Runge theorem.
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Narasimhan, R., Nievergelt, Y. (2001). The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem. In: Complex Analysis in One Variable. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0175-5_5
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DOI: https://doi.org/10.1007/978-1-4612-0175-5_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6647-1
Online ISBN: 978-1-4612-0175-5
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