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

DOI：10.3770/j.issn:2095-2651.2016.06.005

 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

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.

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.