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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Wavelet Analysis And Applications In Economics And Finance, Tian-Xiao He, Tung Nguyen, '15
Wavelet Analysis And Applications In Economics And Finance, Tian-Xiao He, Tung Nguyen, '15
Tian-Xiao He
Construction Of Spline Type Orthogonal Scaling Functions And Wavelets, Tian-Xiao He, Tung Nguyen, '15
Construction Of Spline Type Orthogonal Scaling Functions And Wavelets, Tian-Xiao He, Tung Nguyen, '15
Tian-Xiao He
No abstract provided.
Frames And Spline Framelets, Tian-Xiao He, Tung Nguyen, '15, Nahee Kim, '15
Frames And Spline Framelets, Tian-Xiao He, Tung Nguyen, '15, Nahee Kim, '15
Tian-Xiao He
No abstract provided.
Sequences Of Numbers Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter J.-S. Shiue, Tsui-Wei Weng
Sequences Of Numbers Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter J.-S. Shiue, Tsui-Wei Weng
Tian-Xiao He
Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of the Fibonacci, the Lucas, the Pell, and the Jacobsthal numbers in terms of the generalized Gegenbauer-Humbert polynomial values are given. The applications of the relationship to the construction of identities of number and polynomial value sequences defined by linear recurrence relations are also discussed.
Generalized Exponential Euler Polynomials And Exponential Splines, Tian-Xiao He
Generalized Exponential Euler Polynomials And Exponential Splines, Tian-Xiao He
Tian-Xiao He
Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.
Sequences Of Non-Gegenbauer-Humbert Polynomials Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter Shiue
Sequences Of Non-Gegenbauer-Humbert Polynomials Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter Shiue
Tian-Xiao He
Here,we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given. The applications of the relationship to the construction of identities of polynomial sequences defined by linear recurrence relations are also discussed.
Generalized Stirling Numbers And Generalized Stirling Functions, Tian-Xiao He
Generalized Stirling Numbers And Generalized Stirling Functions, Tian-Xiao He
Tian-Xiao He
Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, and Trujilloet and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Three algorithms for calculating the Stirling numbers based on our generalization are also …
Generalized Zeta Functions, Tian-Xiao He
Generalized Zeta Functions, Tian-Xiao He
Tian-Xiao He
We present here a wide class of generalized zeta function in terms of the generalized Mobius functions and its properties.
A Symbolic Operator Approach To Power Series Transformation-Expansion Formulas, Tian-Xiao He
A Symbolic Operator Approach To Power Series Transformation-Expansion Formulas, Tian-Xiao He
Tian-Xiao He
In this paper we discuss a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalizations, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed.
A Pair Of General Series-Transformation Formulas, Tian-Xiao He, Leetsch Hsu, Peter Shiue
A Pair Of General Series-Transformation Formulas, Tian-Xiao He, Leetsch Hsu, Peter Shiue
Tian-Xiao He
No abstract provided.