A note on generating functions and summation formulae for Meixner polynomials of several variables
Abstract The present paper deals with certain generating functions and various elegant summation formulae for Meixner polynomials of several variables.
Some families of generating functions associated with the Stirling numbers of the second kind
The object of this paper is to present a systematic introduction to (and several interesting applications of) a general result on generating functions (associated with the Stirling numbers of the second kind) for a fairly wide variety of special functions and polynomials in one, two, and more variables. The main results given below are shown to apply not only to the classical orthogonal polynomials including, for example, the Jacobi polynomials (which contain, as their special cases, the Gegenbauer or ultraspherical polynomials, the Legendre or spherical polynomials, and the Chebyshev polynomials of the first and second kinds) and the Laguerre polynomials, and to their various extensions and generalizations studied in recent years, but indeed also to a class of generalized hypergeometric functions, the Lauricella polynomials in several variables, and the familiar Lagrange polynomials which arise in certain problems in statistics. Relevant connections of some of these families of generating functions with various known results are also indicated.
State estimation for integrated vehicle dynamics control
This paper discusses a vehicle controller and a state estimator that was implemented and tested in a vehicle equipped with a combined braking and chassis control system to improve handling. The vehicle dynamics controller consists of a feed forward body roll compensation and a feedback stability controller. The estimator is based on a non-linear vehicle model combined with an extended Kalman filter. The Kalman filter is also connected to an algorithm, which estimates the tyre-road friction coefficient. The developed estimator was tested in a vehicle. Good results were achieved for normal and extreme driving manoeuvers.