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一些新的q-级数恒等式

Some New Identities of q-series
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摘要 通过对称的双边Bailey变换证明了两个新的q-级数恒等式;同时利用q-二项式定理和发生函数法,建立了几个和式的递推关系,并利用已有的q-级数恒等式得到了Ramanujan恒等式的一般形式. Two q-series identities were proved by symmetrical and bilateral Bailey's transform. Several recurrence relations of some summations are established by employing generating functions and q-binomial theorem. A normal form of Ramanujan's identity was given with q-series identities.
作者 刘广军 陈静
出处 《河南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2012年第4期32-34,共3页 Journal of Henan Normal University(Natural Science Edition)
基金 河南省教育厅科学技术研究重点项目(12B110030)
关键词 对称的双边Bailey变换 q-级数恒等式 Ramanujan恒等式 发生函数 symmetrical and bilateral Bailey's transform identities of q-series Ramanujan's identity generating function
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参考文献7

  • 1Bailey W N.Generalised hypergeometric series[M].Cambridge:Cambridge University Press,1935.
  • 2Bailey W N.Identities of the Rogers-Ramanujan type[J].Proc London Math Soc,1949,50(2):1-10.
  • 3Andrews G E,Warnaar S O.The Bailey transform and false theta functions[J].Ramanujan J,2009,14:173-188.
  • 4Gasper G,Rahman M.Basic hypergeometric series,Encyclopedia of Mathematics and Its Applications 35[M].Second Edition.Cambiri-dge:Cambridge University Press,2004.
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  • 7Andrews G E.The Theory of Partitions[M].Cambridge:Cambridge University Press,1998.

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