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.