The Gamma and Zeta Functions
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.
KeywordsEntire Function Analytic Continuation Meromorphic Function Zeta Function Gamma Function
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