We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...

Classical Gon£arov polynomials are polynomials which interpolate derivatives. Delta Gon£arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gon£arov polynomials and univariate delta Gon£arov polynomials to the multivariate setting using umbral calculus. After intro...

Complex Multiplication (CM) method is a frequently used method for the generation of elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this method is the computation of the roots of a special type of class polynomials, called Hilbert polynomials. However, there are several polynomials, called class polynomials, which can be used in the CM method and have much s...

We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...

On the Analogue of the Division Polynomials for Hyperelliptic Curves