Cauchy's theorem (Cauchy–Goursat). Let f be holomorphic on a simply connected open set D ⊆ ℂ. Then for every closed piecewise- smooth contour γ ⊂ D, ∮_γ f(z) dz = 0 "Simply connected" means D has no ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and ...

Glendon College, York University, Toronto, Canada. Although integrals on unbounded contours have been used frequently in complex analysis (see [1], page 214), they have never appeared in the context ...

Abstract: Fundamental to complex analysis is the Cauchy integral theorem, and the derivation of Cauchy-type integrals. For over 40 yr, Cauchy-type integrals have been used to describe analytical ...

Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which ...

This repository provides the PDF, code, and experimental validation for Maryam’s Theorem, a generalization of Cauchy’s projection formula to non-convex surfaces via the Moeini Convexity Measure. The ...

Abstract: An asymptotic property for the median point of Cauchy Mean-value Theorem is discussed in a week condition, and a universal result is obtained. As a deduction, the result be used to an ...