Meromorphic function

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Complex analysis

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Related lectures (13)

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Global View of Dwork's Proof

Explores a 'global' view of Dwork's proof, emphasizing the vanishing of a determinant.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Laurent Series: Definition and Properties

Covers the definition and properties of Laurent series, including convergence and function expansion.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Shell Components in Meromorphic Parameter Spaces

Explores shell components in transcendental parameter planes and attracting cycles.

Analyse IV: Laurent Series and Singularities

Covers Laurent series, singularities, and meromorphic functions, addressing convergence, holomorphicity, and residue theorem applications.

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Residues and Singularities

Covers the calculation of residues, types of singularities, and applications of the residue theorem in complex analysis.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Nyquist Criterion: Stability Analysis

Covers the Nyquist criterion for stability analysis in control systems, using the Nyquist diagram to determine closed loop poles.

Complex Manifolds: GAGA Principle

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

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