Related papers: Approximating tau-functions by theta-functions
We give two kinds of approximation of Lyapunov exponents of rational functions of degree more than one on the projective line over more general fields than that of complex numbers.
A characterization of the Kadomtsev-Petviashvili hierarchy of type C (CKP) in terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy can be identified with the restriction of odd times flows of the KP hierarchy on…
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution…
This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of…
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
We consider a new subclass $\widetilde{\mathcal{K}}_u$ of close-to-convex functions in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$. For this class, we obtain sharp estimates of the Fekete-Szeg\"{o} problem, growth and distortion…
We compute the Hilbert series of the graded algebra of regular functions on a symplectic quotient of a unitary circle representation. Additionally, we elaborate explicit formulas for the lowest coefficients of the Laurent expansion of such…
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
We present a new simple algorithm for efficient, and relatively accurate computation of the Faddeyeva function w(z). The algorithm carefully exploits previous approximations by Hui et al [1978] and Humlicek [1982] along with asymptotic…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
In this paper, we will give estimates for the logarithmic derivative $ \left\vert \frac{f^{\left( k\right) }\left( z\right) }{f\left( z\right) } \right\vert $ where $f$ is a meromorphic function in a region of the form $ D\left( 0,R\right)…
In this paper, we introduce a Kantorovich type generalization of q-Bernstein-Stancu operators. We study the convergence of the introduced operators and also obtain the rate of convergence by these operators in terms of the modulus of…
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial,…
We show how one can obtain rational approximants for $q$-extensions of the harmonic series and the logarithm (and many other similar quantities) by Pad\'e approximation using little $q$-Legendre polynomials and we show that properties of…
In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we…
Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers simultaneously tau-well approximable by infinitely many rationals with denominators in Q but only by finitely many rationals with denominators…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
We present an infinite family of Borwein type $+ - - $ conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series with Macdonald polynomial argument.