on padé approximation of some practical functions

The padé approximation of has special importance in some engineering problems such as investigation of linear time-delayed systems. in this paper a novel method is introduced to construct padé approximation form of some practical functions, such as , with non-integers and , and with non-integer . this method gives a new closed form of padé approximant of these functions by orthogonal polynomials. it introduces also a novel method to reduce the order of an ordinary differential equation. in other words, the method of this paper presents a new method to approximate the solution of an -order ordinary differential equation by an ( )- order ordinary differential equation.