Results 231 to 240 of about 130,034 (274)
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2011
In this lecture, we shall present Cauchy’s integral formula that expresses the value of an analytic function at any point of a domain in terms of the values on the boundary of this domain, and has numerous important applications. We shall also prove a result that paves the way for the Cauchy’s integral formula for derivatives given in the next lecture.
Ravi P. Agarwal +2 more
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In this lecture, we shall present Cauchy’s integral formula that expresses the value of an analytic function at any point of a domain in terms of the values on the boundary of this domain, and has numerous important applications. We shall also prove a result that paves the way for the Cauchy’s integral formula for derivatives given in the next lecture.
Ravi P. Agarwal +2 more
+4 more sources
The College Mathematics Journal, 1990
Our purpose in this note is to illustrate the Cauchy integral formula and the concept of winding number. The software we use is fiz), ver. 4.0, Martin Lapidus, Lascaux Graphics, Bronx, NY, 1988. Many mathematicians and most students are at a loss to picture the graph of even the most elementary complex function.
David P. Kraines +2 more
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Our purpose in this note is to illustrate the Cauchy integral formula and the concept of winding number. The software we use is fiz), ver. 4.0, Martin Lapidus, Lascaux Graphics, Bronx, NY, 1988. Many mathematicians and most students are at a loss to picture the graph of even the most elementary complex function.
David P. Kraines +2 more
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Split Octonionic Cauchy Integral Formula
Advances in Applied Clifford Algebras, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1992
Abstract Armed with Cauchy’s theorem we can prove a host of striking results about holomorphic functions. These stem from the Cauchy formulae which we derive in this chapter. We are then able to prove the following, with relative ease. All this is in sharp contrast to the behaviour of real-valued functions on JR.
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Abstract Armed with Cauchy’s theorem we can prove a host of striking results about holomorphic functions. These stem from the Cauchy formulae which we derive in this chapter. We are then able to prove the following, with relative ease. All this is in sharp contrast to the behaviour of real-valued functions on JR.
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2014
Holomorphic functions on a polydisc are represented by the Cauchy integral of their values on the distinguished boundary of the polydisc.
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Holomorphic functions on a polydisc are represented by the Cauchy integral of their values on the distinguished boundary of the polydisc.
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Quadrature formulas for cauchy principal value integrals
Computing, 1975Quadrature formulas of the Clenshaw-Curtis type, based on the “practical” abscissasx k=cos(kπ/n),k=0(1)n, are obtained for the numerical evaluation of Cauchy principal value integrals $$\int\limits_{ - 1}^1 {(x - a)^{ - 1} } f(x) dx, - 1< a< 1$$ .
Chawla, M. M., Jayarajan, N.
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Cauchy’s Integral Formula for Derivatives
2011In this lecture, we shall show that, for an analytic function in a given domain, all the derivatives exist and are analytic. This result leads to Cauchy’s integral formula for derivatives. Next, we shall prove Morera’s Theorem, which is a converse of the Cauchy–Goursat Theorem.
Ravi P. Agarwal +2 more
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Cauchy Integral Formula for Fuchsian Groups
Complex Analysis and Operator TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Applications of Cauchy’s Integral Formula
1985In this chapter, we return to the ideas of Theorem 7.3 of Chapter III, which we interrupted to discuss some topological considerations about winding numbers. We come back to analysis. We shall give various applications of the fact that the derivative of an analytic function can be expressed as an integral.
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Cauchy’s Formula and Its Applications
1997Abstract This chapter studies Cauchy’s Formula and its applications. Cauchy’s Formula says that the values of f on L rigidly determine its values everywhere inside L. The chapter offers two explanations, both of which are firmly rooted in Cauchy’s Theorem. It then looks at infinite differentiability and Taylor series.
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