Electronic Proceedings of the 12^th Asian Technology Conference in Mathematics

Abstract for 12806

What is the function y^(n) = y ?

Authors: Shin Watanabe

Affiliations: Tokai University

Keywords:

We will be using Taylor Series with technological tools to explore

the functions which could be a solution of the differential equation

y^(n) = y. There are functions, which are number of n.

Before we use the Fundamental Theorem of Algebra, which states

that every non-zero single-variable polynomial, with complex

coefficients, has exactly as many complex roots as its degree, if

repeated roots are counted up to their multiplicity. We will use the

fact that there are n linearly independent vectors to form a basis

in the space of R^n to solve the equation.