Among their topics are holomorphic functions, Taylor and Laurent series
, spaces of functions, Fourier analysis, and linear operators in Hilbert spaces: the finite-dimension and infinite-dimensional cases.
All of the computed examples in this paper, except for the Laurent series example in the last section, are performed using variations of this reflection algorithm.
Crowdy and Marshall  give a Laurent series method for evaluating the prime function for general circle domains where the convergence condition above need not hold.
The slit maps exist in all cases independently of their infinite product expansion and can be evaluated efficiently with Laurent series .
Chapters cover the complex plane, complex line integrals, applications of the Cauchy theory, Laurent series
, the argument principle, the geometric theory, harmonic functions, infinite series and products, and analytic continuation.
, the ships remained in service in their original condition, although they did receive an austere refit under the Destroyer Life Extension Program (DELEX), in the mid-eighties.
The methodology [Gil, 1995] that underlies this proposal is based on a generalization of the PA for formal Laurent series [Bultheel, 1987].
The fifth section presents a generalization of the PA for formal Laurent series and its application to TF models with expectations.
Another question arises for comparing the results obtained in this paper from the T table method with those obtained from other identification procedures related to the PA for formal Laurent series, for example, the generalized e-algorithm [Gill, 1995], those proposed in the identification of doubly infinite series, and, especially, those in the identification of a TF model with expectations.
They cover complex numbers and their geometry, complex differentiability, Cauchy integral theorem and its consequences, Taylor and Laurent series
, and harmonic functions.
They begin by describing complex numbers and their elementary properties, including power series, powers and logarithms and the geometric properties of simple functions, analytic functions such as differentiation and integration in the complex frame, Cauchy's integral formula, Taylor and Laurent series
and analytic continuation, contour integration, conformal mapping, including the Joukowsky and Schwarz-Christoffel transformations, special functions such as the gamma function and the Lefendre and Bessel functions, asymptotic methods such as that of Laplace, transform methods such as Fourier transforms, and special techniques such as the Weiner-Hopf methods, the kernel decomposition and using approximate kernels.
It also discusses elementary aspects of complex analysis such as the Cauchy integral theorem, the residue theorem, Laurent series
, the Riemann mapping theorem, and more advanced material selected from Riemann surface theory.