Results 211 to 220 of about 2,481 (254)

The Laurent Expansion Without Cauchy's Integral Theorem [PDF]

open access: yesCanadian Mathematical Bulletin, 1972
Since Cauchy's time the theory of analytic functions of a complex variable has depended on complex integration theory, and in particular on the fundamental integral theorem (1825) and integral formulas bearing his name. Cauchy defined an analytic function to be one which had a continuous first derivative in a region D, and showed that an analytic ...
Paul R. Beesack
openaire   +3 more sources

On Cauchy Integral Theorem for Quaternionic Slice Regular Functions

Complex Analysis and Operator Theory, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J OSCAR González-Cervantes
exaly   +3 more sources

Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem [PDF]

open access: yesNumerical Algorithms, 2008
It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, that two general families of definite integrals can be evaluated in closed form and are expressible only in terms of the Hurwitz zeta function and elementary
Djurdje Cvijovic   +2 more
exaly   +2 more sources

The Cauchy Integral Theorem

The American Mathematical Monthly, 2007
Theorem. Let D be a domain in the complex plane, f(z) an analytic function in D, C a closed curve that is described by a continuously differentiable function z(s) (0 < s < 1) with z(0) = z(l) and zf(0) = z'(\). Suppose that C is homotopic in D to a point, meaning that there is a continuous function z(s, t) (0 < s < I, 0 < t < 1) with z(0, t) = z(l, t ...
openaire   +2 more sources

A Voronovskaya Type Theorem for Poisson–Cauchy Type singular operators [PDF]

open access: yesJournal of Mathematical Analysis and Applications, 2010
In this article we continue with the study of approximation properties of smooth Poisson–Cauchy Type singular integral operators over the real line. We produce Voronovskaya Type results and give some quantitative results regarding the rate of convergence
George A Anastassiou, Răzvan A Mezei
exaly   +2 more sources

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