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Meromorphic Functions

In: Complex Analysis and Dynamics in One Variable with Applications

Author

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  • Luis T. Magalhães

    (University of Lisbon, Instituto Superior Técnico)

Abstract

Isolated singularities of complex functions (removable, poles, and essential), Laurent series and its annulus of convergence, relationship with Fourier series, meromorphic functions, the residues theorem, the Jordan lemma and applications to real functions improper integrals, the Argument Principle, Rouché theorem, Jensen formula. Exercises, including on the Gamma function, Mittag–Leffler theorem, infinite products, Weierstrass factorization theorem, holomorphic functions factorization theorem, Riemann Zeta function, asymptotic expansions, and with applications to fluid dynamics, aerodynamics, and linear systems analysis and control including root locus, Nyquist contour and stability criterion, polar and Nichols diagrams, Proportional–Integral–Derivative and Proportional–Derivative controllers.

Suggested Citation

  • Luis T. Magalhães, 2025. "Meromorphic Functions," Springer Books, in: Complex Analysis and Dynamics in One Variable with Applications, chapter 0, pages 143-188, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-64999-8_8
    DOI: 10.1007/978-3-031-64999-8_8
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