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WZ方法与一类组合和的渐近估计问题 被引量：2

WZ METHOD AND THE ASYMTOTIC ESTIMATES FOR A KIND OF COMBINATORIAL SUM
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摘要 通过使用WZ理论中有关结果,给出了当n→+∞时,sum from k=0 to rn (pn k)^(p-r)/(p-2r)(pn rn)(其中p、r均为一般的正整数参数且p>2r)的一个相对初等的新证明. 3y using the results from WZ theory, a new and relatively elementary proof is given for,∑n=0^rn（Pn k）～p-r/p-2r（pn rn） as n→＋∞,where p and r are generic parameters being positive integers.
作者 陈奕俊
机构地区 华南师范大学数学科学学院
出处 《华南师范大学学报（自然科学版）》 CAS 北大核心 2009年第1期1-5,共5页 Journal of South China Normal University(Natural Science Edition)
关键词 定超几何和 不定超几何和 WZ方法 渐近估计 definite hypergeometric sum indefinite hypergeometric sum WZ method asymptotic estimate
分类号 O157.1 [理学—基础数学]
  • 相关文献

参考文献14

  • 1WILF H S, ZEILBERGER D. Rational functions Certify Combinatorial identities [ J]. J of Amer Math Soc, 1990, 3 : 147 - 158.
  • 2PETKOVSEK M, WILF H S, ZEILBERGER D. A = B [ M]. Massachusetts : A K Peters Ltd, 1996.
  • 3ZEILBERGER D. Closed form (Pun intended) [J]. Contemporary Mathematics, 1993,143:579 - 607.
  • 4AMDEBERHAN T. Faster and faster series for ζ ( 3 ) [ J]. Elect J of Combin, 1996,3 :#R13.
  • 5AMDEBERHAN T, ZEILBERGER D. Hypergeometric series acceleration via the WZ method [ J ]. Elect J of Combin, 1997,4 :#R3.
  • 6EKAHD S B, ZEILBERGER D. A WZ proof of Ramanujan's formula for π[C]//RASSIAS J M. Geometry,Analysis and Mechanics. Singapore: World Scientific, 1994.
  • 7GUILLERA J. Some binomial series obtained by the WZ method[ J ]. Adv in Applied Mathematics, 2002,29 : 599 - 603.
  • 8GUILLERA J. Generators of some Ramanujan's formulas [J]. The Ramanujan Journal, 2006,11 ( 1 ) :41 -48.
  • 9WILF H S. Accelerated series for Universal constants by WZ method[ J]. J of Discrete Mathematics and Theoretical Computer Science, 1999,3 : 189 - 192.
  • 10陈奕俊.WZ方法的两个应用[J].华南师范大学学报（自然科学版）,2008,40(1):13-19. 被引量：3

二级参考文献22

  • 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
  • 2陈奕俊.Gosper算法与一类组合和是否有闭形式的问题[J].数学学报（中文版）,2007,50(4):831-840. 被引量：2
  • 3PETKOVSEK M, WILFH S, ZEILBERGER D. A=B[M]. Massachusetts: A K Peters Wellesley,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): 1- 7.
  • 5PAULE P, SCHORN M. A mathematica version of Zeilberger's algorithm for proving binomial coefficient identities[J]. J Symbolic Computation, 1995,20:673-698.
  • 6GRAHAM R L, KNUTH D E, PATASHNIK O. Concrete Mathematics[M]. Massachusetts: Addison Wesley , 1994.
  • 7EGORYCHEV G P. Integral representation and the computation of combinatorialsums[A]. In: Translations of Mathematical Monographs of AMS(Volume 59)[M]. Rhode Island: AMS, 1984.
  • 8GOOD I J. Saddle- point methods for the multinomial distribution[J]. Ann Math Statist, 1957, 28:861- 881.
  • 9PETKOVSEK M,WILF H S, ZEILBERGER D. A =B [M]. Massachusetts:A K Peters Ltd,1996.
  • 10WILF H S, ZEILBERGER D. Rational functions certify combinatorial identities[ J]. J Amer Math Soc, 1990, 3 : 147 - 158.

共引文献4

同被引文献35

  • 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
  • 2WILF H S, ZEILBERGER D. Rational functions certify combinatorial identifies[ J ]. J of Amer Math Soc, 1990, 3 : 147 - 158.
  • 3PETKOVSEK M, WILF H S, ZEILBERGER D. A = B [M]. Massachusetts:A K Peters,1996.
  • 4GESSEL I. Finding identities with the WZ method[J]. J of Symbolic Computation , 1995,70:537 - 566.
  • 5ZEILBERGER D. Closed form ( pun intended ! ) [ J ].Contemporary Mathematics , 1993,143:579 - 607.
  • 6AMDEBERHAN T. Faster and faster convergent series for ξ(3) [J]. Elect J of Combin, 1996,3 :#R13.
  • 7AMDEBERHAN T, ZEILBERGER D. Hypergeometric series acceleration via the WZ method [ J ]. Elect J of Combin , 1997,4 :#R3.
  • 8GUILLERA J. Some binomial series obtained by the WZ method[J]. Advances in Applied Mathematics, 2002, 29:599 - 603.
  • 9GUILLERA J. Generators of some Ramanujan formulas [J]. The Ramanujan Journal ,2006,1:41 -48.
  • 10WILF H S. Accelerated series for universal constants by WZ method[J]. J of Discrete Mathematics and Theoretical Computer Science , 1999,3 : 189 - 192.

引证文献2

二级引证文献5

华南师范大学学报（自然科学版）
2009年 第1期

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