Open AccessComplex Variable Theorems for Finding Zeroes and Poles of Transcendental Functions
Author(s) -
D. V. Giri
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1334/1/012005
Subject(s) - mathematics , simple (philosophy) , polynomial , variable (mathematics) , zero (linguistics) , extension (predicate logic) , argument (complex analysis) , transcendental function , function (biology) , transcendental equation , order (exchange) , transcendental number , calculus (dental) , mathematical analysis , discrete mathematics , differential equation , computer science , medicine , philosophy , linguistics , biochemistry , chemistry , dentistry , epistemology , finance , evolutionary biology , economics , biology , programming language
The principle of the argument or the winding number is useful in finding the number of zeros of an analytic function in a given contour. A simple extension of this theorem yields relationships involving the locations of these zeros! The resulting equations can be solved very accurately for the zero locations, thus avoiding initial, guess values, which are required by many other techniques. Examples such as a 20th order polynomial, natural frequencies of a thin wire will be discussed.