Related papers: A Proof of a Recursion for Bessel Moments

Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…

Let x(n) be a recurrence relation. The main purpose of this article is to determine a recurrence for powers of x(n).

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we…

We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towards (dis)proving a conjecture of Helson. We also prove…

We present a formula for the convolution $\delta_{C_1}*\delta_{C_2}$ of two circle impulses. The derivation uses a classical addition theorem for Bessel functions.

In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…

Assuming the existence of Siegel zeros, we prove that there exists an increasing sequence of positive integers for which Chowla's Conjecture on $k$-point correlations of the Liouville function holds. This extends work of Germ\'an and…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We investigate certain positive random variables having moments of Gamma type. Some necessary and some sufficient conditions are given for their existence. In particular, we observe that the Weber-Schafheitlin formula for the Bessel…

Taking $t$ at random, uniformly from $[0,T]$, we consider the $k$th moment, with respect to $t$, of the random variable corresponding to the $2\beta$th moment of $\zeta(1/2+ix)$ over the interval $x\in(t, t+1]$, where $\zeta(s)$ is the…

A theorem of Bayer and Teichmann implies that if a finite real multisequence \beta = \beta^(2d) has a representing measure, then the associated moment matrix M_d admits positive, recursively generated moment matrix extensions M_(d+1),…

We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.

We extend the recursion formula for matrix Bessel functions, which we obtained previously, to superspace. It is sufficient to do this for the unitary orthosymplectic supergroup. By direct computations, we show that fairly explicit results…

We prove certain identities between relative Bessel functions attached to irreducible unitary representations of $\mathrm{PGL}_2(\mathbb{C})$ and Bessel functions attached to irreducible unitary representations of $\mathrm{SL}_2…

An explicit expression of the k-th derivative of the Bessel function $J_\nu(z)$, with respect to its order $\nu$, is given. Particularizations for the cases of positive or negative $\nu$ are considered.

We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].

Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen,and…

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…

In this paper, we prove the local converse conjecture of Jacquet over p-adic fields for GL(n) using Bessel functions.

We prove positivity results about linearization and connection coefficients for Bessel polynomials. The proof is based on a recursion formula and explicit formulas for the coefficients in special cases. The result implies that the…