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Abel’s lemma on summation by parts and partial q-series transformations 被引量：1

Abel’s lemma on summation by parts and partial q-series transformations
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摘要 The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established. The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.
作者 CHU WenChang WANG ChenYing
机构地区 Department of Applied Mathematics
出处 《Science China Mathematics》 SCIE 2009年第4期720-748,共29页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation for the Youth (Grant No. 10801026)
关键词 Abel’s lemma on SUMMATION by PARTS basic HYPERGEOMETRIC SERIES well-poised SERIES quadratic SERIES cubic SERIES QUARTIC SERIES reciprocal relation Abel’s lemma on summation by parts basic hypergeometric series well-poised series quadratic series cubic series quartic series reciprocal relation 33D15 05A15
分类号 O211.3 [理学—概率论与数理统计]
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参考文献17

  • 1Wenchang Chu.Abel’s lemma on summation by parts and Ramanujan’s 1ψ1-series identity[J]. Aequationes mathematicae . 2006 (1-2)
  • 2Hardy G H.Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work. . 1978
  • 3Chu W.Abel’s lemma on summation by parts and Ramanujan’s 1ψ1-series identity. Aequationes Mathematicae . 2006
  • 4Rahman M.Some quadratic and cubic summation formulas for basic hypergeometric series. Canadian Journal of Mathematics . 1993
  • 5Stromberg K R.An Introduction to Classical Real Analysis. . 1981
  • 6W. N. Bailey,Generalized hypergeometric series,Cambridge Math.Tract No. . 1935
  • 7Gasper,G.,Rahman,M. Basic Hypergeometric Series . 2004
  • 8Slater,L.J. Generalized hypergeometric functions . 1966
  • 9Bailey,W. N.Series of hypergeometric type which are infinite in both directions. The Quarterly Journal of MaThematics Oxford . 1936
  • 10Chu,W. C.Bailey’s very well-poised 6ω6-series identity. Journal of Combinatorial Theory Series A . 2006

同被引文献6

  • 1GASPER G, RAHMAN M. Basic Hypergeometric Series [M]. Cambridge: Cambridge University Press, 2004.
  • 2SLATER L J. Generalized Hypergeometric Functions [M]. Cambridge: Cambridge University Press, 1966.
  • 3CHU W. Inversion techniques and combinatorial identities [J]. Bollettino U M I, 1993(7): 737-760.
  • 4CHU W. Inversion techniques and combinatorial identities: Jackson's q-analogue of the Dougall-Dixon theorem and the dual formulae [J]. Compositio Mathematica, 1995, 95(1): 43-68.
  • 5GASPER G. Summation, transformation, and expansion formulas for bibasic series [J]. Trans Amer Math Soc, 1989, 312(1): 257-277.
  • 6GASPER G, RAHMAN M. An indefinite bibasic summation formula and some quadratic, cubic and quartic nnrnrnatlon and transformation formulas [Jl. Can J Math 1990. 42: 1-27.

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Science China Mathematics
2009年 第4期

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