General Formula for limit of square function at infinity

Determination of the limit value of a function is an important things. Basically, the limit is used to look at the "properties" function value around the point. In this paper, we provide the general formula for the limit of square root function at infinite. This general formula comes from the development of a commonly known base formula. We use some simple algebra theorems to develop it. The result is very similar to the basic formula for limit of square root function at infinite

The Characteristics of the First Kind of Chebyshev Polynomials and its Relationship to the Ordinary Polynomials

In this article, we discuss the Chebyshev Polynomial and its characteristics. The second order difference equation and the process obtaining the explicit solution of the Chebyshev polynomial have been given for each real number. The symmetry and orthogonality of the Chebyshev polynomial has also been demonstrated using the explicit solutions obtained. Furthermore, we have also given how to approx the polynomial function using the Chebyshev polynomials

Statistical properties of an estimator for the mean function of a compound cyclic Poisson process in the presence of linear trend

The problem of estimating the mean function of a compound cyclic Poisson process with linear trend is considered. An estimator of this mean function is constructed and investigated. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the linear trend is assumed to be positive, but its value is unknown. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. Asymptotic bias and variance of the proposed estimator are computed, when the size of interval indefinitely expands