Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

Asymptotic Distributions of the Zeros of a Family of Hypergeometric Polynomials

The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Gauss hypergeometric polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Gauss hypergeometric polynomials, 2F1(−n, a;−n+ b; z), where n is a nonnegative integer. Owing to the connection between the classical Jacobi poly...

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

On polynomials related with Hermite - - Pade approximations to the exponential function

We investigate the polynomials P n ; Q m and R s , having degrees n; m and s respectively, with P n monic, that solve the approximation problem E nms (x) := P n (x)e ?2x + Q m (x)e ?x + R s (x) = O(x n+m+s+2) as x ! 0: We give a connection between the coeecients of each of the polynomials P n ; Q m and R s and certain hypergeometric functions, which leads to a simple expression for Q m in the c...

On the average number of sharp crossings of certain Gaussian random polynomials

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.