Wave phenomena around inflection points are studied from a new point of view in order to co-ordinate inflective shapes analytically. Inflective co-ordinate systems are used to compute the exact solutions. The differential equations obtained using these recently introduced co-ordinate systems are solved by extending the usual separation method. These extensions lead to the development of special functions and series, and the achieved results give an exact physical meaning to the inflection points. In addition, electromagnetic waves are characterised around an inflection point.