D. D. SOMASHEKARA,K. N. VIDYA,S. L. SHALINI.On Finite Forms of Certain Bilateral Basic Hypergeometric Series and Their Applications[J].数学研究及应用,2016,36(6):665~672
On Finite Forms of Certain Bilateral Basic Hypergeometric Series and Their Applications
On Finite Forms of Certain Bilateral Basic Hypergeometric Series and Their Applications
投稿时间:2016-04-18  最后修改时间:2016-07-29
DOI:10.3770/j.issn:2095-2651.2016.06.005
中文关键词:  bilateral basic hypergeometric series  finite forms  theta functions  sums of squares and sums of triangular numbers
英文关键词:bilateral basic hypergeometric series  finite forms  theta functions  sums of squares and sums of triangular numbers
基金项目:The first author is thankful to University Grants Commission(UGC), India for the financial support under the grant SAP-DRS-1-NO.F.510/2/DRS/2011 and the second author is thankful to UGC for awarding the Basic Science Research Fellowship, No.F.25-1/2014-15(BSR)/No.F.7-349/2012(BSR).
作者单位
D. D. SOMASHEKARA Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru-570006, India 
K. N. VIDYA Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru-570006, India 
S. L. SHALINI Department of Mathematics, Mysuru Royal Institute of Technology, Lakshmipura, Srirangapatna-571438, India 
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中文摘要:
      In this paper we derive finite forms of the summation formulas for bilateral basic hypergeometric series $_3\psi_3$, $_4\psi_4$ and $_5\psi_5$. We therefrom obtain the summation formulae obtained recently by Wenchang CHU and Xiaoxia WANG. As applications of these summation formulae, we deduce the well-known Jacobi's two and four square theorems, a formula for the number of representations of an integer $n$ as sum of four triangular numbers and some theta function identities.
英文摘要:
      In this paper we derive finite forms of the summation formulas for bilateral basic hypergeometric series $_3\psi_3$, $_4\psi_4$ and $_5\psi_5$. We therefrom obtain the summation formulae obtained recently by Wenchang CHU and Xiaoxia WANG. As applications of these summation formulae, we deduce the well-known Jacobi's two and four square theorems, a formula for the number of representations of an integer $n$ as sum of four triangular numbers and some theta function identities.
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