Related papers: Bessel function asymptotics: a relation due to Lom…
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…
We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.
A pair of linearly independent asymptotic solutions are constructed for the second-order linear difference equation {equation*} P_{n+1}(x)-(A_{n}x+B_{n})P_{n}(x)+P_{n-1}(x)=0, {equation*} where $A_n$ and $B_n$ have asymptotic expansions of…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We introduce the notion of $p$-adic asymptotics, or $p$-asymptotics, to the context of finite-index subgroup and subalgebra enumeration. For finitely generated groups and finite-dimensional algebras, we connect these asymptotics with the…
Asymptotic approximations of Jacobi polynomials are given for large values of the $\beta$-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the…
We review the relation between compact asymptotic spectral measures and certain positive asymptotic morphism on locally compact spaces via asymptotic Riesz representation theorem, as introduced by Martinez and Trout [3]. Applications to…
We provide a new, simple general proof of the formulas giving the infinite sums $\sigma(p,\nu)$ of the inverse even powers $2p$ of the zeros $\xi_{\nu k}$ of the regular Bessel functions $J_{\nu}(\xi)$, as functions of $\nu$. We also give…
We give an elementary proof of the existence of an asymptotic expansion in powers of $k$ of the Bergman kernel associated to $L^k$, where $L$ is a positive line bundle. We also give an algorithm for computing the coefficients in the…
The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in…
We study the asymptotic behaviour of the cohomology of subgroups $\Gamma$ of an algebraic group $G$ with coefficients in the various irreducible rational representations of $G$ and raise a conjecture about it. Namely, we expect that the…
Using the saddle-point method, we compute an asymptotic, as $y \rightarrow \infty$, for the $K$-Bessel function $K_{r + i t}(y)$ with positive, real argument $y$ and of large complex order $r+it$ where $r$ is bounded and $t = y \sin \theta$…
We prove that for $\nu>n-1$ all zeros of the $n$th derivative of Bessel function of the first kind $J_{\nu}$ are real and simple. Moreover, we show that the positive zeros of the $n$th and $(n+1)$th derivative of Bessel function of the…
It is shown in this paper that there is a fine correlation of the third order between the values of the functions $Z[\vp_1(t)]$ and $\tilde{Z}^2(t)$ which corresponds to two collections of disconnected sets. The corresponding new asymptotic…
We obtain an asymptotic formula for the mean value of L-functions associated to cubic characters over F_q[t]. We solve this problem in the non-Kummer setting when q=2 (mod 3) and in the Kummer case when q=1 (mod 3). The proofs rely on…
Given a principal bundle with a connection, we look for an asymptotic expansion of the holonomy of a loop in terms of its length. This length is defined relative to some Riemannian or sub-Riemannian structure. We are able to give an…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we…
We consider a function $G(\lambda, z)$, entire in $\lambda$, which interpolates the derivatives of the Gamma function in the sense that $G(m, z) = \Gamma^{(m)}(z)$ for any integer $m \geq 0$ and we calculate the asymptotics of $G(\lambda,…
We show that the number of positive integers $n\leq N$ such that $\mathbb{Z}/(n^2+n+1)\mathbb{Z}$ contains a perfect difference set is asymptotically $N/\log{N}$.