Journal ArticleJournal of Combinatorial Theory Series A · August 1, 2025
Given a positive integer n, consider a permutation of n objects chosen uniformly at random. In this permutation, we collect maximal subsequences consisting of consecutive numbers arranged in ascending order called blocks. Each block is then merged, and aft ...
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Journal ArticleCommunications in Statistics Theory and Methods · January 1, 2025
The hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special ca ...
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Journal ArticleJournal of Physics A Mathematical and Theoretical · November 15, 2024
Lattice geometries and random walks on them are of great interest for their applications in different fields such as physics, chemistry, and computer science. In this work, we focus on multi-headed lattices and study properties of the Green functions for t ...
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Journal ArticleComptes Rendus Mathematique · January 1, 2024
The q-analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the q-Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the q-Euler numbers. It i ...
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Journal ArticleContributions to Discrete Mathematics · January 1, 2024
We calculate the Hankel determinants of certain sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries’ natural and deep connection with Bernoul ...
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Journal ArticleOpen Mathematics · January 1, 2023
The method of brackets is a symbolic approach to the computation of integrals over R n {{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This ...
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Journal ArticleContributions to Discrete Mathematics · January 1, 2023
Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit, the situation often changes significantly. In this paper we use classical ...
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Journal ArticleInternational Journal of Number Theory · March 1, 2022
We evaluate the Hankel determinants of various sequences related to Bernoulli and Euler numbers and special values of the corresponding polynomials. Some of these results arise as special cases of Hankel determinants of certain sums and differences of Bern ...
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Journal ArticleIntegers · January 1, 2022
Let a and b, with a < b, be two level sites of a general random walk. If we partition [a, b] into n arbitrary subintervals with endpoints a < a1 < a2 < · · · < an−1 < b, then the hitting time from a to b can also be decompo ...
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Journal ArticleJournal of Mathematical Analysis and Applications · May 1, 2021
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials B2k+1(x) and the Euler polynomials E2k+ν(x), for ν=0,1,2. In the pro ...
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Journal ArticleOpen Mathematics · September 16, 2020
AbstractThe method of brackets, developed in the context of evaluation of integrals coming from Feynman diagrams, is a procedure to evaluate definite integrals over the half-line. This method consists of a s ...
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Journal ArticleMathematics in Computer Science · September 1, 2020
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, i ...
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Journal ArticleInternational Journal of Number Theory · April 2020
We introduce a symbolic representation of [Formula: see text]-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions ...
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Journal ArticleOpen Mathematics · September 27, 2017
AbstractThe method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discus ...
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Journal ArticleInternational Journal of Number Theory · May 2016
The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials admit extensions to this new family. A specific expression involving th ...
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Journal ArticleOpen Mathematics · January 1, 2016
AbstractThe method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used ...
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Journal ArticleJournal of the Australian Mathematical Society · April 2015
AbstractThe finite Fourier transform of a family of orthogonal polynomials is the usual transform of these polynomials extended by
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Journal ArticleInternational Journal of Number Theory · November 2014
The hypergeometric zeta function is defined in terms of the zeros of the Kummer function M(a, a+b; z). It is established that this function is an entire function of order 1. The classical factorization theorem of Hadamard gives an expression as an ...
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Journal ArticleEntropy · August 4, 2014
In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control ...
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Journal ArticleMathematica Slovaca · October 1, 2013
AbstractIn this paper, we mainly consider the first and second arc length variational problems on the exponential statistical manifold, and give the variational formulae. ...
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