指数型有理插值与q-级数互反关系 |
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引用本文: | 初文昌.指数型有理插值与q-级数互反关系[J].计算数学,1989,11(4):428-433. |
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作者姓名: | 初文昌 |
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作者单位: | 中国科学院系统科学研究所 |
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摘 要: | 成立. 显然,在上式中取q=1,便退化为Could-Hsu反演公式.在2—5]中曾应用后者构造插值级数,并对其中一类广义牛顿插值级数进行系统的研究.作者在此基础上应用(1.3)构造指数型插值函数. 首先引进q差分算子△_q,定义
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关 键 词: | 指数型 有理插值 q-级数 互反关系 |
EXPONENTIAL-TYPE RATIONAL INTERPOLATION AND Q-INVERSE SERIES RELATIONS |
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Affiliation: | Chu Wen-chang Institute of Systems Science, Academia Sinica |
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Abstract: | As applications of q-series inversions, this paper proposes a method for constructing expon-ential-type rational interpolation formulas. By means of q-difference operation, a representationtheorem is proved which states that this kind of interpolation formula can be used to expressexponential-type rational functions. For q=1, these results reduce to the generalized Newtoninterpolation series theory developed by Hsu and Yang extensively. As a natural extension ofthis method, a class of bivariate q-inverse relations containing five sets of free parameters areestablished. Applications to bivariate interpolation formulas of non-tensor product form in theone-dimensional case are also presented. |
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