Abstract
Suppose we are given a function f which is analytic in a region D. We will say that f can be continued analytically to a region D 1 that intersects D if there exists a function g, analytic in D 1 and such that g = f throughout \( D_1 \cap D_2 \). By the Uniqueness Theorem (6.9) any such continuation of f is uniquely determined. (It is possible, however, to have two analytic continuations g 1 and g 2 of a function f to regions D 1 and D 2 respectively with \( g_1 \ne g_2 \) throughout \( D_1 \cap D_2 \). See Exercise 1.)
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Bak, J., Newman, D.J. (2010). Analytic Continuation; The Gamma and Zeta Functions. In: Complex Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7288-0_18
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DOI: https://doi.org/10.1007/978-1-4419-7288-0_18
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