Location of the Zeros of Certain Complex‐Valued Harmonic Polynomials
Hunduma Legesse Geleta, Oluma Ararso Alemu
Abstract
Finding the approximate region containing all the zeros of analytic polynomials is a well‐studied problem. But the number of the zeros and regions containing all the zeros of complex‐valued harmonic polynomials is relatively a fresh research area. It is well known that all the zeros of analytic trinomials are enclosed in some annular sectors that take into account the magnitude of the coefficients. Following Kennedy and Dehmer, we provide the zero inclusion regions of all the zeros of complex‐valued harmonic polynomials in general, and in particular, we bound all the zeros of some families of harmonic trinomials in a certain annular region.
Topics & Concepts
TrinomialMathematicsZero (linguistics)HarmonicComplex planePure mathematicsMathematical analysisDiscrete mathematicsPhysicsLinguisticsQuantum mechanicsPhilosophyAnalytic and geometric function theoryMathematical functions and polynomialsHolomorphic and Operator Theory