相关论文: The Ap\'ery Numbers as a Stieltjes Moment Sequence
We exploit results from the classical Stieltjes moment problem to bring out the totality of all the information regarding phase insensitive nonclassicality of a state as captured by the photon number distribution p_n. Central to our…
The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical…
The Stieltjes moment problem is studied in a new framework within the general Gelfand-Shilov spaces defined via weight sequences. The novelty consists of allowing for a naturally larger target space for the moment mapping, which sends a…
Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other…
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…
In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.
The Stieltjes constants \gamma_k(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function \zeta(s,a) about s=1. We present series representations of these constants of interest to theoretical…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\le j) are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and…
We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for…
Let $A(n,m)$ denote the Eulerian numbers, which count the number of permutations on $[n]$ with exactly $m$ descents. It is well known that $A(n,m)$ also counts the number of permutations on $[n]$ with exactly $m$ excedances. In this report,…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
In this note we use the analogy between the Catalan sequence and the Rueppel sequence to derive a variety of conjectures surrounding the Hankel transforms of a number of sequences closely related to the Rueppel sequence. Use is made of the…
The classical sequence of Bernoulli numbers is known to the the sequence of moments of a family of orthogonal polynomials. Some similar statements are obtained for another sequence of rational numbers, which is similar in many ways to the…
A combinatorial interpretation is provided for the moments of characteristic polynomials of random unitary matrices. This leads to a rather unexpected consequence of the Keating and Snaith conjecture: the moments of $\mid\xi(1/2+it)\mid$…
A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.
Given a finite nonempty sequence of integers S, by grouping adjacent terms it is always possible to write it, possibly in many ways, as S = X Y^k, where X and Y are sequences and Y is nonempty. Choose the version which maximizes the value…
We find Stieltjes-type and Jacobi-type continued fractions for some "master polynomials" that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results…
In this note we give a combinatorial and non-computational proof of the asymptotics of the integer moments of the moments of the characteristic polynomials of Haar distributed unitary matrices as the size of the matrix goes to infinity.…
A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known…