ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff's series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.  

ON AN EXTENSION OF ABEL-GONTSCHAROFF＇S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.  

On the Applications of the Linear Recurrence Relationships to Pseudoprimes

We present here some results on the applications of linear recursive sequences of order $2$ to the Fermat pseudoprimes, Fibonacci pseudoprimes, and Dickson pseudoprimes.  

Matrix Representation of Recursive Sequences of Order $3$ and Its Applications

Here presented is a matrix representation of recursive number sequences of order $3$ defined by $a_n=pa_{n-1}+qa_{n-2}+ra_{n-3}$ with arbitrary initial conditions $a_0,$ $a_1=0$, and $a_2$ and their special cases of Padovan number sequence and Perrin number sequence with initial conditions $a_0=a_1=0$ and $a_2=1$ and $a_0=3$, $a_1=0$, and $a_2=2$, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.  

Application of Polynomial Interpolation in the Chinese Remainder Problem

This paper presents an application of polynomial interpolation in the solution of the Chinese Remainder Problem for bother integers and polynomials.  

A Unified Approach to Construct a Class of Daubechies Orthogonal Scaling Functions

We use Lorentz polynomials to give an efficient way to prove Daubechies’ results on the existence of spline type orthogonal scaling functions and to evaluate a class of Daubechies scaling functions in a unified approach.  

递推数列的非线性表达式的构造

受徐文［9］的启发,本文建立一类Lucas数列的非线性表达式.作者还应用该数列与其它2阶线性递推数列的关系,将上述表达式推广到众多2阶递推数列.  

Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials

Here presented are the definitions of(c)-Riordan arrays and(c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials.The characterization of(c)-Riordan arrays by means of the A-and Z-sequences is given,which corresponds to a horizontal construction of a(c)-Riordan array rather than its definition approach through column generating functions.There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of(c)-Riordan arrays,which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences.The sequence characterization is applied to construct readily a(c)-Riordan array.In addition,subgrouping of(c)-Riordan arrays by using the characterizations is discussed.The(c)-Bell polynomials and its identities by means of convolution families are also studied.Finally,the characterization of(c)-Riordan arrays in terms of the convolution families and(c)-Bell polynomials is presented.  

A Unified Approach to Generalized Stirling Functions

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, k-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous well-known Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed,which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions.