The electromagnetic phenomena around inflection points are studied from a new point of view in order to co-ordinate inflective shapes analytically. To obtain the exact solutions, new coordinate systems are defined. The family of these co-ordinate systems is, on the whole, collected as inflective co-ordinate systems. The differential equations obtained using these new coordinate systems are solved by extending the usual separation method. These extensions bring out new, special functions and series. The results achieved clarify the physics of inflection points. In addition, the electrostatic field is calculated around inflection points.