The third Appell function for one large variable

The Appell ’ S Function F 2 for Large Values of Its Variables

The second Appell’s hypergeometric function F2(a, b, b ′, c, c′;x, y) has a Mellin convolution integral representation in the region (x + y) < 1 and a > 0. We apply a recently introduced asymptotic method for Mellin convolution integrals to derive three asymptotic expansions of F2(a, b, b ′, c, c′;x, y) in decreasing powers of x and y with x/y bounded. For certain values of the real parameters ...

Turan’s Inequality for Appell Polynomials

Function Fields of One Variable over PAC Fields

Function Fields of One Variable over PAC Fields by Moshe Jarden, Tel Aviv University and Florian Pop, University of Pennsylvania In this note we give evidence for a conjecture of Serre and a conjecture of Bogomolov. Conjecture II of Serre considers a field F of characteristic p with cd(Gal(F )) ≤ 2 such that either p = 0 or p > 0 and [F : F ] ≤ p and predicts that H(Gal(F ), G) = 1 (i.e. each p...

A Variable Structure Observer Based Control Design for a Class of Large scale MIMO Nonlinear Systems

This paper fully discusses how to design an observer based decentralized fuzzy adaptive controller for a class of large scale multivariable non-canonical nonlinear systems with unknown functions of subsystems’ states. On-line tuning mechanisms to adjust both the parameters of the direct adaptive controller and observer that guarantee the ultimately boundedness of both the tracking error and tha...

Limit Theorems for Bivariate Appell

Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...