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It is shown that a pair of inverse relations can be constructed by the suitable application of Faà di Bruno's formula for finding higher order derivatives of composite functions. Various examples illustrating the applications of inverse relations are presented.  相似文献
2.
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.  相似文献
3.
In this paper a connective study of Gould‘s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould‘s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff‘s remainder and a new form of it are demonstrated, and also illustrated with several examples.  相似文献
4.
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.  相似文献
5.
This paper presents an application of polynomial interpolation in the solution of the Chinese Remainder Problem for bother integers and polynomials.  相似文献
6.
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.  相似文献
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