Related papers: Asymptotics of Bivariate Analytic Functions with A…
We prove asymptotic formulas for Toeplitz determinants generated by functions with sequences of Fourier coefficients belonging to weighted Orlicz sequence classes. We concentrate our attention on the case of nonvanishing generating…
We give asymptotic expansions for the moments of the $M_2$-rank generating function and for the $M_2$-rank generating function at roots of unity. For this we apply the Hardy-Ramanujan circle method extended to mock modular forms. Our…
Block and G\"ottsche introduced a Laurent polynomial multiplicity to count tropical curves. Itenberg and Mikhalkin then showed that this multiplicity leads to invariant counts called tropical refined invariants. Recently, Brugall\'e and…
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl…
Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…
We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many…
In this paper, by using asymptotic expansions of oscillatory integrals with positive real power phase functions in one variable, we obtain asymptotic expansions of oscillatory integrals with phase functions expressed by a product of…
The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized that this study…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
We calculate full asymptotic expansions of prime-independent multiplicative functions on additive arithmetic semigroups that satisfy a strong form of Knopfmacher's axioms. When applied to the semigroup of unlabeled graphs, our method yields…
Normal forms for wide classes of closed IL formulas were given in [4]. Here we quantify asymptotically, in exact numbers, how wide those classes are. As a consequence, we show that the "majority" of closed IL formulas have GL-equivalents,…
We present a formula describing the asymptotics of a class of multivariate orthogonal polynomials with hyperoctahedral symmetry as the degree tends to infinity. The polynomials under consideration are characterized by a factorized weight…
We propose a formula for finding the horizontal, oblique or curvilinear asymptote of any rational polynomial function of any positive degree, as a sum of matrix determinants formed directly from the coefficients of the terms in the given…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Considering one of the fundamental notions of Bers' theory of pseudoanalytic functions the generating pair via an intertwining relation we introduce its generalization for biquaternionic equations corresponding to different first-order…
In this article, $q$-regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
One relates factorization of bivariate polynomials to singularities of projective plane curves. One proves that adjoint polynomials permit to solve the recombinations of the modular factors induced by the absolute and rational…
The purpose of this paper is to describe asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices with singular generating functions. The formulas are similar to those of the analogous problem for finite Toeplitz…
The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in…