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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
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.
Some Dense Subsets Of Real Numbers And Their Applications, Tian-Xiao He, Peter Shiue, Xiaoya Zha
Some Dense Subsets Of Real Numbers And Their Applications, Tian-Xiao He, Peter Shiue, Xiaoya Zha
Tian-Xiao He
We give a collection of subsets which are dense in the set of real numbers. Several applications of the dense sets are also presented.
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.