Wave phenomena around inflection points are studied from a new point of vie
w in order to co-ordinate inflective shapes analytically. Inflective co-ord
inate systems are used to compute the exact solutions. The differential equ
ations obtained using these recently introduced co-ordinate systems are sol
ved 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, electromag
netic waves are characterised around an inflection point.