On Padé Approximation of Some Practical Functions

The Padé approximation of Tz e 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 z e, (1 -z)α (1 +z)β with non-integers α and β, ln(1+z) and (1+z)β with non-integer β. 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 n -order ordinary differential equation by an (n-1)- order ordinary differential equation.