Related papers: A Proof of a Recursion for Bessel Moments
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an…
We show that classical processes corresponding to operators what satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell's inequality for their covariances can be extended…
We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are…
Following previous investigations by {\"U}st{\"u}nel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random change of time is invertible on the Poisson space. As a…
Recently Conrey, Farmer, and Zirnbauer developed the L-functions Ratios conjecture, which gives a recipe that predicts a wealth of statistics, from moments to spacings between adjacent zeros and values of L-functions. The problem with this…
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
In this paper we extend the results given in \cite{Mo18} to the $n$-dimensional case the fractional powers of Bessel operators. Moreover, we established a Liouville type theorems for these operators. This extend the result obtained in…
We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot,…
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We explicitly determine the Ap\'ery limits for the sums of powers of binomial coefficients. As an application, we prove a weak version of Franel's conjecture on the order of the recurrences for these sequences. Namely, we prove the…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof…
In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since…
Using Voronoi's truncated formula for $\Delta(x)$ involving Bessel functions, the first author derives an asymptotic formula for the eighth-power moments with an error term of order $O\left(X^{3 - \frac{1}{254} + \varepsilon}\right)$
We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…