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We consider the notion of integrals depending on a parameter. Unexpectedly, this notion turns out to be quite nontrivial in complex analysis: even in the situation, when the integrand is a single-valued form, the integral is a ramified function as a rule. For this reason, parametric integrals in complex analysis are also called ramified integrals. The aim of this chapter is to describe this phenomenon in examples and then present the general theory of such integrals.
KeywordsRiemannian Surface Analytic Continuation Homology Class Holomorphic Form Compact Complex Manifold
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