12 citations · 27 across the 22 of their papers we have counts for
24 papers
Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers
Lin Jiu, Yihang Yin
When exploring the Hankel determinant of the sequence , where is the -th Bernoulli number, we obtained two interesting results. The first one applie…
New central -binomial identities
Shane Chern, Karl Dilcher, Lin Jiu
We establish several new series evaluations involving the central -binomial coefficients, with the inspiration coming from earlier work by Vignat and one of the authors on the l…
Multi-headed lattices and Green functions
Qipin Chen, Shane Chern, Lin Jiu
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 focu…
Leading coefficient in the Hankel determinants related to binomial and -binomial transforms
Shane Chern, Lin Jiu, Shuhan Li +1
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to…
Information geometry and -parallel prior of the beta-logistic distribution
Lin Jiu, Linyu Peng
The hyperbolic secant distribution has several generalizations with applications in finance. In this study, we explore the dual geometric structure of one such generalization, name…
A central limit theorem for a card shuffling problem
Shane Chern, Lin Jiu, Italo Simonelli
Given a positive integer , consider a random permutation of the set . In , we look for sequences of consecutive integers that appear in adjacent positi…
Hankel determinants and Jacobi continued fractions for -Euler numbers
Shane Chern, Lin Jiu
The -analogs of Bernoulli and Euler numbers were introduced by Carlitz. Similar to the recent results on the Hankel determinants for the -Bernoulli numbers established by Cha…
Random Walk Models for Nontrivial Identities of Bernoulli and Euler Polynomials
Lin Jiu, Italo Simonelli, Heng Yue
We consider the -dimensional reflected Brownian motion and -dimensional Bessel process and the general models. By decomposing the hitting times of consecutive sites into loop…
Hankel Determinants of Certain Sequences Of Bernoulli Polynomials: A Direct Proof of an Inverse Matrix Entry from Statistics
Lin Jiu, Ye Li
We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regre…
Hankel Determinants of shifted sequences of Bernoulli and Euler numbers
Karl Dilcher, Lin Jiu
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…
Orthogonal polynomials and Hankel Determinants for certain Bernoulli and Euler Polynomials
Karl Dilcher, Lin Jiu
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials …
Calculation and Properties of Zonal Polynomials
Lin Jiu, Christoph Koutschan
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, represent…
On b-ary binomial coefficients with negative entries
Lin Jiu, Diane Y. H. Shi
Abstract. We generalize the -ary binomial coefficients with negative entries, which is based on the generating function obtained in early work. Besides an explicit expression in…
Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials
Lin Jiu, Diane Yahui Shi
We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are Meixner-Pollaczek polynomials with certain arguments and constant fac…
Integral representations of equally positive integer-indexed harmonic sums at infinity
Lin Jiu
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and…
Matrix Representation for Multiplicative Nested Sums
Lin Jiu, Diane Yahui Shi
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the ind…
On Binomial Identities in Arbitrary Bases
Lin Jiu, Christophe Vignat
We extend the digital binomial identity as given by Nguyen el al. to an identity in an arbitrary base , by introducing the ary binomial coefficients. We then study the prope…
Pochhammer Symbol with Negative Indices. A New Rule for the Method of Brackets
Ivan Gonzalez, Lin Jiu, Victor H. Moll
The 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 Besse…
On the Method of Brackets: Rules, Examples, Interpretations and Modifications
Lin Jiu
The method of brackets, consisting of a small number of heuristic rules, was created by Ivan Gonzalez for the evaluation of definite integrals appearing in the resolution of Feynma…
A Symbolic Approach to Some Indentities for Bernoulli-Barnes Polynomials
Lin Jiu, Victor H. Moll, Christophe Vignat
A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.
The finite Fourier transform of classical polynomials
Atul Dixit, Lin Jiu, Victor H. Moll +1
The finite Fourier transform of a family of orthogonal polynomials , is the usual transform of the polynomial extended by outside their natural domain. Explicit expre…
Identities for generalized Euler polynomials
Lin Jiu, Victor H. Moll, C. Vignat
For , let be the Chebyshev polynomial of the first kind. Expressions for the sequence of numbers , defined as the coefficients in the expa…
Recursion Rules for the Hypergeometric Zeta Functions
Alyssa Byrnes, Lin Jiu, Victor H. Moll +1
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…
The unimodality of a polynomial coming from a rational integral. Back to the original proof
Tewodros Amdeberhan, Atul Dixit, Xiao Guan +2
A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.