We consider families of analytic functions with Taylor coefficients-polynomials in the parameter λ: fλ(z) = ∑∞ k=0 ak(λ)z k, ak ∈ C[λ]. Let R(λ) be the radius of convergence of fλ. The “Taylor domination” property for this family is the inequality of the following form: for certain fixed N and C and for each k ≥ N + 1 and λ, |ak(λ)|R(λ) ≤ C max i=0,...,N |ai(λ)|R(λ). Taylor domination property ...

We apply the new framework for modularity of false theta functions developed by second author and Nazaroglu to study asymptotic behavior Taylor coefficients Jacobi forms. The examples we generate moments rank unimodal sequences. For two types sequences, prove series moments.

Characterization of Schur functions in terms of their Taylor coefficients is due to C. Carathéodory and I. Schur. We discuss the boundary analogue of this problem.

By a deformation of the integers we mean a sequence x = {xn, n ∈ N} of polynomials in one or more variables and with integral coefficients, having the property that there exists some value q0 of the variables such that ∀n ∈ N, xn(q0) = n. The quantum integers xn = ∑n−1 l=0 q l are a typical example of a deformation of the integers. Another example is given by the version of the Chebyshev polyno...

van der Corput's inequality is extended and refined by using Euler-Maclaurin formula and other analytic techniques.

We derwe and analyze the properties of Euler-Maclaurin expansions for the differences / ~ / s'(log.~) " /(.~. Qilfj is a combination of one-dimensional generalized trapezoidal rule approximations. 1. ~NlKOL)UC110N In this work we are intcrcstcd in deriving Euler-Maclaurin expansions for the singular double integrals where W(X) = x'(Iog x)'. s >-l.s'=O. 1. (1.3) and f(.~,~l) is as many times dif...

A local lattice point counting formula, and more generally a local Euler-Maclaurin formula follow by comparing two natural families of meromorphic functions on the dual of a rational vector space V , namely the family of exponential sums (S) and the family of exponential integrals (I) parametrized by the set of rational polytopes in V . The paper introduces the notion of an interpolator between...

This paper presents explicit formulae for multivariate Maclaurin-Lagrange M : Kn1×n2×...×nd → Kn1×n2×...×nd and Maclaurin-Newton P : Kn1×n2×...×nd → Kn1×n2×...×nd transformations with respect to points whose coordinates form geometric sequences. Moreover, efficient algorithms for these transformations are given. Both of them perform computations with a running time of O (∏d j=1 nj · log ∏d j=1 ...