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Two new transformation formulas of basic hypergeometric series

Authors:	Caihuan Zhang Zhizheng Zhang

Affiliation:	^a Department of Mathematics, Luoyang Normal University, Luoyang 471022, PR China ^b Department of Mathematics, Dalian University of Technology, Dalian 116024, PR China ^c College of Mathematics and Information Science, Henan University, Kaifeng 475001, PR China

Abstract:	By means of a modified version of Cauchy's method for obtaining bilateral series identities, two new transformation formulas for bilateral basic hypergeometric series are derived. These contain several important identities for basic hypergeometric series as special cases, including the nonterminating q-Saalschütz summation, Bailey's very well-poised summation and the nonterminating Watson transformation.

Keywords:	Basic hypergeometric series Three terms transformation on nonterminating mmlsi2" onclick=" submitCitation('/science?_ob=MathURL& _method=retrieve& _eid=1-s2.0-S0022247X0700282X& _mathId=si2.gif& _pii=S0022247X0700282X& _issn=0022247X& _acct=C000051805& _version=1& _userid=1154080& md5=2806453e964373645453537ef65ae9eb')" style=" cursor:pointer " alt=" Click to view the MathML source" title=" Click to view the MathML source" > 14" border=" 0" style=" vertical-align:bottom" width=" 23" alt=" View the MathML source" title=" View the MathML source" src=" http://ars.els-cdn.com/content/image/1-s2.0-S0022247X0700282X-si2.gif" >-series Bailey's transformation on nonterminating very well-poised mmlsi3" onclick=" submitCitation('/science?_ob=MathURL& _method=retrieve& _eid=1-s2.0-S0022247X0700282X& _mathId=si3.gif& _pii=S0022247X0700282X& _issn=0022247X& _acct=C000051805& _version=1& _userid=1154080& md5=71821147b54d554c3bdfe97ba6f23793')" style=" cursor:pointer " alt=" Click to view the MathML source" title=" Click to view the MathML source" > 15" border=" 0" style=" vertical-align:bottom" width=" 29" alt=" View the MathML source" title=" View the MathML source" src=" http://ars.els-cdn.com/content/image/1-s2.0-S0022247X0700282X-si3.gif" >-series
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