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：20160418 最后修改时间：20160729 
DOI：10.3770/j.issn:20952651.2016.06.005 
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 SAPDRS1NO.F.510/2/DRS/2011 and the second author is thankful to UGC for awarding the Basic Science Research Fellowship, No.F.251/201415(BSR)/No.F.7349/2012(BSR). 
作者  单位  D. D. SOMASHEKARA  Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru570006, India  K. N. VIDYA  Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru570006, India  S. L. SHALINI  Department of Mathematics, Mysuru Royal Institute of Technology, Lakshmipura, Srirangapatna571438, 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 wellknown 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 wellknown 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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