Related papers: A Note on Jain basis functions
We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
1 : We use properties of the Stern Sequence for numerical computations of moments $\int^1_0 t^n d?(t)$ associated to Minkowski's Question Mark function.
In this paper, we first derive an inequality involving central moments for n real numbers, which in turn provides an extension of Theorem 2.2 of Wolkowicz and Styan [18]. Furthermore, we present refinements of various inequalities obtained…
The first order nonlinear ODE \dot \phi(t) + \sin\phi(t)=q(t),q(t)=B+A\cos\omega t, where A,B,\omega are real constants, is considered, the transformation converting it to a second order linear homogeneous ODE with polynoimial coefficients…
Moment problems and orthogonal polynomials, both meant in a single real variable, belong to the oldest problems in Classical Analysis. They have been developing for over a century in two parallel, mostly independent streams. During the last…
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…
The problem of recovering a moment-determinate multivariate function $f$ via its moment sequence is studied. Under mild conditions on $f$, the point-wise and $L_1$-rates of convergence for the proposed constructions are established. The…
For any positive integer n, a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equation of order n. The n roots are the values of the appropriate function from that…
In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.
Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
The article is devoted to investigation of the classes of functions belonging to the gaps between classes $P_{n+1}(I)$ and $P_{n}(I)$ of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
All integrals needed to evaluate the correlated wave functions with polynomial terms of inter-electronic distance are included. For this form of the wave function, the integrals needed can be expressed as a product of integrals involving at…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
We study the number of queries needed to identify a monotone Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$. A query consists of a 0-1-sequence, and the answer is the value of $f$ on that sequence. It is well-known that the number of…
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and…