On the Uniform Distribution of the Roots of Certain Polynomials

Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

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

On Classifications of Random Polynomials

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...

Uniform Convergence Behavior of the Bernoulli Polynomials

The roots of Bernoulli polynomials, Bn(z), when plotted in the complex plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987 that, on compact subsets of C, the Bernoulli polynomials asymptotically behave like sine or cosine. Here we establish the asmptotic behavior of Bn(nz), compute the distribution of real roots of Bernoulli polynomials and show that, properly rescal...

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...