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Papers by Tian-Xiao He

Research paper thumbnail of q-Analogs of Riordan Arrays

Research paper thumbnail of The Riordan Group and Applications

Springer monographs in mathematics, 2022

Research paper thumbnail of Orthogonal Polynomials

Springer monographs in mathematics, 2022

Research paper thumbnail of Combinatorial Sums and Inversions

Research paper thumbnail of Generalized Riordan Arrays

Springer monographs in mathematics, 2022

Research paper thumbnail of Extraction of Coefficients and Generating Functions

Springer monographs in mathematics, 2022

Research paper thumbnail of Extensions of the Riordan Group

Springer monographs in mathematics, 2022

Research paper thumbnail of Polynomials that have Golden Ratio Zeros

When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are fu... more When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are functions of the Fibonacci sequence in terms of the other coefficients, which characterize the polynomials completely. These functions are used to derive some Fn, Ln, and golden ratio identities. In many cases, this is generalized to the Lucas functions Un and Vn, with associated quadratic root pair. A new type of geometric progression is introduced.

Research paper thumbnail of A unified approach for the Catalan matrices by using Riordan arrays

Linear Algebra and its Applications, 2018

Research paper thumbnail of Characterization of Riordan Arrays by Special Sequences

Springer monographs in mathematics, 2022

Research paper thumbnail of Representations of positive integers as sums of arithmetic progressions, II

Notes on Number Theory and Discrete Mathematics, Apr 27, 2023

Research paper thumbnail of On the Applications of the Linear Recurrence Relationships to Pseudoprimes

Research paper thumbnail of Divisibility of Generalized Catalan Numbers and Raney Numbers

Journal of Computational Analysis and Applications, 2019

Research paper thumbnail of An approach to the construction of linear divisibility sequences of higher orders

Journal of Integer Sequences, 2017

Research paper thumbnail of On generalised Möbius inversion formulas

Bulletin of The Australian Mathematical Society, Feb 1, 2006

Research paper thumbnail of Application of Polynomial Interpolation in the Chinese Remainder Problem

Research paper thumbnail of On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach

arXiv (Cornell University), Jun 21, 2021

Research paper thumbnail of On an extension of Abel-Gontscharoff’s expansion formula

Analysis in Theory and Applications, Dec 1, 2005

Research paper thumbnail of Divisibility of the Sums of the Power of Consecutive Integers

arXiv (Cornell University), Apr 15, 2023

Research paper thumbnail of A Pair of General Series-Transformation Formulas

Journal of Mathematical Research and Exposition, 2005

ABSTRACT This note is devoted to present two general series-transformation formulas for formal se... more ABSTRACT This note is devoted to present two general series-transformation formulas for formal series defined over ℂ, given in terms of the generalized Eulerian functions. The method to be used to deduce both formal expansion formulas follows from a recent paper of the authors and D. C. Torney [J. Comput. Appl. Math. 177, No. 1, 17–33 (2005; Zbl 1064.65002)]. The technical details should appear in a forthcoming paper.

Research paper thumbnail of q-Analogs of Riordan Arrays

Research paper thumbnail of The Riordan Group and Applications

Springer monographs in mathematics, 2022

Research paper thumbnail of Orthogonal Polynomials

Springer monographs in mathematics, 2022

Research paper thumbnail of Combinatorial Sums and Inversions

Research paper thumbnail of Generalized Riordan Arrays

Springer monographs in mathematics, 2022

Research paper thumbnail of Extraction of Coefficients and Generating Functions

Springer monographs in mathematics, 2022

Research paper thumbnail of Extensions of the Riordan Group

Springer monographs in mathematics, 2022

Research paper thumbnail of Polynomials that have Golden Ratio Zeros

When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are fu... more When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are functions of the Fibonacci sequence in terms of the other coefficients, which characterize the polynomials completely. These functions are used to derive some Fn, Ln, and golden ratio identities. In many cases, this is generalized to the Lucas functions Un and Vn, with associated quadratic root pair. A new type of geometric progression is introduced.

Research paper thumbnail of A unified approach for the Catalan matrices by using Riordan arrays

Linear Algebra and its Applications, 2018

Research paper thumbnail of Characterization of Riordan Arrays by Special Sequences

Springer monographs in mathematics, 2022

Research paper thumbnail of Representations of positive integers as sums of arithmetic progressions, II

Notes on Number Theory and Discrete Mathematics, Apr 27, 2023

Research paper thumbnail of On the Applications of the Linear Recurrence Relationships to Pseudoprimes

Research paper thumbnail of Divisibility of Generalized Catalan Numbers and Raney Numbers

Journal of Computational Analysis and Applications, 2019

Research paper thumbnail of An approach to the construction of linear divisibility sequences of higher orders

Journal of Integer Sequences, 2017

Research paper thumbnail of On generalised Möbius inversion formulas

Bulletin of The Australian Mathematical Society, Feb 1, 2006

Research paper thumbnail of Application of Polynomial Interpolation in the Chinese Remainder Problem

Research paper thumbnail of On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach

arXiv (Cornell University), Jun 21, 2021

Research paper thumbnail of On an extension of Abel-Gontscharoff’s expansion formula

Analysis in Theory and Applications, Dec 1, 2005

Research paper thumbnail of Divisibility of the Sums of the Power of Consecutive Integers

arXiv (Cornell University), Apr 15, 2023

Research paper thumbnail of A Pair of General Series-Transformation Formulas

Journal of Mathematical Research and Exposition, 2005

ABSTRACT This note is devoted to present two general series-transformation formulas for formal se... more ABSTRACT This note is devoted to present two general series-transformation formulas for formal series defined over ℂ, given in terms of the generalized Eulerian functions. The method to be used to deduce both formal expansion formulas follows from a recent paper of the authors and D. C. Torney [J. Comput. Appl. Math. 177, No. 1, 17–33 (2005; Zbl 1064.65002)]. The technical details should appear in a forthcoming paper.

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