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Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of power series including some old ones and more new ones. 相似文献
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本文研究了一类复合型幂级数展开式,证明了一个收敛性定理并举例说明其应用.在注记中指出了可进一步研究的问题. 相似文献
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We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs. 相似文献
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The method of non-standard analysis(NSA) is used to construct a pair of hyperstandard reciprocal formulas involving certain non-standard difference operators with realnumber orders.Our main result consists of some extensions of earlier results appearing previously [5].An essential meaning of the paper is to indicate the fact that only the basic idea of NSA is applicable to the construction of a unified pattern that may have certain applications to both the analysis and the number theory. 相似文献
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This paper provides a pair of summation formulas for a kind of combinatorial series involvingak+b m as a factor of the summand. The construction of formulas is based on a certain series transformation formula [2, 7, 9] and by making use of the C-numbers [3]. Various consequences and examples including several remarkable classic identities are presented to illustrate some applications of the formulas obtained. 相似文献
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本文给出了Poincar\'{e}直觉主义连续统的一种超标准模型[PC],并证明了三条基本性质. [PC]是模型(PC)的深化和改进.作为其应用,文中还概述了子模型$\overline{R}$ (非Cantor型连续统)上的一种非标准微积分. 相似文献