Abstract
We now come to a situation where the natural way to define a function is not through a power series but through an integral depending on a parameter. We shall give a natural condition when we can differentiate under the integral sign, and we can then use Goursat’s theorem to conclude that the holomorphic function so defined is analytic.
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© 1999 Springer Science+Business Media New York
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Lang, S. (1999). The Gamma and Zeta Functions. In: Complex Analysis. Graduate Texts in Mathematics, vol 103. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3083-8_15
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DOI: https://doi.org/10.1007/978-1-4757-3083-8_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3135-1
Online ISBN: 978-1-4757-3083-8
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