An approximation property of Gaussian functions

Abstract

Using the power series method, we solve the inhomogeneous linear first order differential equation $$ y'(x) + lambda (x-mu) y(x) = sum_{m=0}^infty a_m (x-mu)^m, $$ and prove an approximation property of Gaussian functions.

Keywords

• Linear first order differential equation
• power series method
• Gaussian function
• approximation
• Hyers-Ulam stability
• local Hyers-Ulam stability