Related papers: Asymptotic approximation of central binomial coeff…

Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form…

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

We consider a regularised Fermi projection of the Hamiltonian of the massless Dirac equation at Fermi energy zero. The matrix-valued symbol of the resulting operator is discontinuous in the origin. For this operator, we prove Szeg\H{o}-type…

Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…

In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\mu$a such that, for any…

A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly…

Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindel\"of, which belong to an attractive but somewhat neglected chapter of complex analysis. One of the…

Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example,…

For each positive integer n, we determine the set of symmetric functions f for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all sufficiently large primes p. Our determination is conditional on a conjecture…

We discuss the relationship between ratio asymptotics for general orthogonal polynomials and the asymptotics of the associated Bergman shift operator. More specifically, we consider the case in which a measure is supported on an infinite…

We consider the number of partitions of $n$ whose Young diagrams fit inside an $m \times \ell$ rectangle; equivalently, we study the coefficients of the $q$-binomial coefficient $\binom{m+\ell}{m}_q$. We obtain sharp asymptotics throughout…

The Stieltjes constants $\gamma_n$ appear in the coefficients in the Laurent expansion of the Riemann zeta function $\zeta(s)$ about the simple pole $s=1$. We present an asymptotic expansion for $\gamma_n$ as $n\rightarrow \infty$ based on…

In 1927 P\'olya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function $\zeta(s)$ at its point of symmetry. This hyperbolicity has been proved for degrees $d\leq 3$. We…

We present a geometric approach to the asymptotics of the Legendre polynomials $P_{k,n+1}$, based on the Szeg\"o kernel of the Fermat quadric hypersurface, and leading to complete asymptotic expansions holding on expanding subintervals of…

In recent years, the Tian-Zelditch asymptotic expansion for the equivariant components of the Szeg\"{o} kernel of a polarized complex projective manifold, and its subsequent generalizations in terms of scaling limits, have played an…

The paper proves a generalization of Wintner's theorem on the asymptotics of summation functions to the case of summation functions with nonlinear asymptotics. The class of arithmetic functions that have a logarithmic asymptotic mean is…

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of $|x|^p$ on two symmetric intervals. Note, that in addition, we get asymptotics…

We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of applications, making progress on several old problems. As a…

We investigate asymptotic polynomial approximation for a class of weighted Bloch functions in the unit disc. Our main result is a structural theorem on asymptotic polynomial approximation in the unit disc, in the flavor of the classical…