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ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA 被引量：1

ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA
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摘要 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. 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.
作者 Tianxiao He Leetsch C. Hsu Peter J. S. Shiue
机构地区 Illinois Wesleyan University Dalian University of Technology University of Nevada Las Vegas
出处 《Analysis in Theory and Applications》 2005年第4期359-369,共11页 分析理论与应用（英文刊）
基金 This paper is a talk on the <International Conference at Analysis in Theory and Applications> held in Nanjing, P. R. China, July, 2004.
关键词 Abel-Gontscharoff＇s Expansion Formula Abel-Gontscharoff-Gould polynomial multivariate Abel-Gontscharoff interpolation higher dimensional dot product annihilation coefficients Abel-Gontscharoff＇s Expansion Formula, Abel-Gontscharoff-Gould polynomial, multivariate Abel-Gontscharoff interpolation, higher dimensional dot product annihilation coefficients
分类号 O17 [理学—基础数学]
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  • 1Gontscharoff, V L , Research on the Successive Derivatives of Analytic Functions (French),Ann Sci Ecole Normale, 47(1930), 1-78.
  • 2Gould, H W , Annihilation coefficients, Analysis, Combinatorics and Computing, (T X He,P J S Shiue and Z Li (eds)), Nova Sci Publ Inc , New York, 2002, 205-223.
  • 3Halphen, G H , On Abel's Series, Bull. S M France, 10(1882), 67-87.
  • 4Hsu, L C , A General Expansion Formula, Analysis, Combinatorics and Computing, (T X He, P L S Shiue and Z Li(eds)), Nova Sci Publ Inc , New York, 2002, 252-258.
  • 5Lorentz, G G. Jetter, K and Riemenschneider, S D , Birkhoff Interpolation, Encyclopedia of Mathematics and Applications, Addison-Welsey Publ Company, London, 1983.
  • 6Mhaskar, H N and Pai, D V , Fundamentals of Approximation Theory, CRC Press, New York, 2000.
  • 7Pincherle, S , On a Series of Abel(French), Acta Mathematik, 28(1904), 225-233.
  • 8Comtet, L. Advanced Combinatorics, Dordrecht Reidel Publ. Company, 1974.
  • 9Davis; P J , Interpolation and Approximation, Blaisdell Publ. Company, New York, 1963.
  • 10Gontscharoff, V L , Theory of Interpolation and Approximation, (Russian), Moscow, 1954.

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Analysis in Theory and Applications
2005年 第4期

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