Results 211 to 220 of about 88,173 (262)

The Cauchy Integral Formula

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, Vivian Y. Kraines, David A. Smith   +2 more
openaire   +1 more source

Split Octonionic Cauchy Integral Formula

Advances in Applied Clifford Algebras, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Quadrature formulas for cauchy principal value integrals

Computing, 1975
Quadrature 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.
openaire   +1 more source

Cauchy Integral Formula

2014
Holomorphic functions on a polydisc are represented by the Cauchy integral of their values on the distinguished boundary of the polydisc.
openaire   +1 more source

Cauchy’s Integral Formula for Derivatives

2011
In 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, Kanishka Perera, Sandra Pinelas   +2 more
openaire   +1 more source

Cauchy Integral Formula for Fuchsian Groups

Complex Analysis and Operator Theory
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

The Cauchy integral formula and distributional integration

Complex Variables and Elliptic Equations, 2018
ABSTRACTWe study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable.
openaire   +1 more source

Classroom Computer Capsule: The Cauchy Integral Formula

The College Mathematics Journal, 1990
(1990). Classroom Computer Capsule: The Cauchy Integral Formula. The College Mathematics Journal: Vol. 21, No. 4, pp. 327-329.
David P. Kraines, Vivian Y. Kraines, David A. Smith   +2 more
openaire   +1 more source

Applications of Cauchy’s Integral Formula

1985
In 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.
openaire   +1 more source

Cells of Harmonicity and Generalized Cauchy Integral Formulae

Proceedings of the London Mathematical Society, 1990
A detailed analysis of the geometry of cells of harmonicity associated to particular types of totally real manifolds lying in \(\mathbb C^ n\) is given. In particular, we show that when n is even, and greater than two, then the Huygens principle may be used over these manifolds. This result is applied to show how the generalized Cauchy integral formula
openaire   +1 more source