Abstract
In this chapter we present an overview of the theory of complex variables, which is required for an understanding of the complex inversion formula discussed in Chapter 4. Along the way, we establish the analyticity of the Laplace transform (Theorem 3.1) and verify the differentiation formula (1.15) of Chapter 1 for a complex parameter (Theorem 3.3).
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© 1999 Springer Science+Business Media New York
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Schiff, J.L. (1999). Complex Variable Theory. In: The Laplace Transform. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22757-3_3
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DOI: https://doi.org/10.1007/978-0-387-22757-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-7262-3
Online ISBN: 978-0-387-22757-3
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