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Gosper算法与一类组合和是否有闭形式的问题 被引量：2

Gosper's Algorithm and the Problem Whether a Kind of Combinatorial Sum Has Closed Form
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摘要 本文由Gosper算法研究了一类形如f_(p,r,x)(n)=∑_(k=0)^(rn)((?))x^k的组合和是否有闭形式的问题。 In this paper, by using Gosper＇s algorithm, I studied the problem whether a kind of combinatorial sum f（p,r,x）（n）=∑（k=0）^（rn）（pn k ））x^k has closed form.
作者 陈奕俊
机构地区 华南师范大学数学科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2007年第4期831-840,共10页 Acta Mathematica Sinica：Chinese Series
关键词 Gosper算法 Gosper方程 闭形式 Gosper＇s algorithm Gosper＇s equation closed form
分类号 O157.1 [理学—基础数学]
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参考文献9

  • 1Chen Y. J., Zeilberger's algorithm, Petkovsek's algorithm and the problem whether a kind of combinatorial sum have closed form, Journal of South China Normal University (Natural Science Edition), to appear
  • 2Petkovsek M., Wilf H. S., Zeilberger D., A = B,,AK Peters Ltd., M. assachusetts: Wellesley, 1996.
  • 3Petkovgek M., Will H. S., When can the sum of (1/p)th of the binomial coefficients have closed form, Electronic Journal of Combinatorics, 1997, 2: #R21.
  • 4Chen Y. J., WZ-method, integral representation and the problem of asymptotic estimates for a kind of combinatorial sum, Journal of South China Normal University (Natural Science Edition), 2004, 3:29 36
  • 5Graham R. L., Knuth D. E., Patashnik O., Concrete mathematics, Massachusetts: Addison Wesley, 1994.
  • 6Andrewsv G. E., Askey R., Roy R., Special functions, Cambridge: Cambridge University Press, 1999.
  • 7von zur Gathen J., Gerhard J., Mordern computer algebra, Cambridge: Cambridge University Press, 1999.
  • 8Koepf W., Hypergeometric summation, Braunschweig/Wiesbaden: Vieweg, 1998.
  • 9Gosper R. W. Jr., Decision procedure for indefinite hypergeometric summation, Proc. Natl. Acad. Sci. USA, 1978, 75:40-42

同被引文献25

  • 1陈奕俊.WZ方法、积分表示与一类组合和的渐近估计问题[J].华南师范大学学报（自然科学版）,2004,36(3):29-36. 被引量：4
  • 2EGORYCHEV G P.Integral Representation and the Computation of Combinatorial Sums[M].Rhode Island:Translations of Mathematical Monographs of AMS,Vol 59,1984.
  • 3PETKOVSEK M,WILF H S,ZEILBERGER D.A=B[M].Massachusetts:A K Peters Ltd,1996.
  • 4PETKOVSEK M,WILF H S.When can the sum of (1/p)th of the binomial coefficients has closed form?[J].Electronic Journal of Combinatorics,1997,4(2):251-257.
  • 5ZEILBERGER D.Gauss's 2F1(1) cannot be generalized to 2F1(x)[J].J Comp Appl Math,1992,39:379-382.
  • 6ZEILBERGER D.Closed form (pun intended!)[J].Contemporary Mathematics,1993,143:579-607.
  • 7AMDERBERHAN T,ZEILBERGER D.Hypergeometric series acceleration via the WZ method[J].Elect J of Combin,1997,4(2):16-19.
  • 8ABRAMOV S A,PETKOVSEK M.D′Alembertian solutions of linear differential and difference equations[C]∥GIESBRECHT M.Proc ISSAC′94.New York:ACM Press,1994:169-174.
  • 9MCINTOSH R J.Recurrences for alternating sums of powers of binomial coefficients[J].Journal of Combinatorial theory SeriesA,1993,63:223-233.
  • 10GOULD H W.Sums of powers of binomial coefficients via Legendre polynomial[J].Combinatorica,2004,73:33-43.

引证文献2

二级引证文献4

数学学报（中文版）
2007年 第4期

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