q Difference equations of moment integrals for transformational identities and generating functions

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1、JournalofDifferenceEquationsandApplicationsISSN:1023-6198(Print)1563-5120(Online)Journalhomepage:http://www.tandfonline.com/loi/gdea20q-DifferenceequationsofmomentintegralsfortransformationalidentitiesandgeneratingfunctionsJianCao&TianxinCaiTocitethisarticle:JianCao&Tian

2、xinCai(2014)q-Differenceequationsofmomentintegralsfortransformationalidentitiesandgeneratingfunctions,JournalofDifferenceEquationsandApplications,20:12,1592-1608,DOI:10.1080/10236198.2014.961444Tolinktothisarticle:http://dx.doi.org/10.1080/10236198.2014.961444Publishedon

3、line:26Sep2014.SubmityourarticletothisjournalArticleviews:67ViewrelatedarticlesViewCrossmarkdataFullTerms&Conditionsofaccessandusecanbefoundathttp://www.tandfonline.com/action/journalInformation?journalCode=gdea20Downloadby:[NewYorkUniversity]Date:25December2016,At:17:39

4、JournalofDifferenceEquationsandApplications,2014Vol.20,No.12,15921608,http://dx.doi.org/10.1080/10236198.2014.961444q-Differenceequationsofmomentintegralsfortransformationalidentitiesandgeneratingfunctionsa,ba,1JianCao*andTianxinCaiaDepartmentofMathematics,ZhejiangUniver

5、sity,HangzhouCity,ZhejiangProvince310027,bP.R.China;DepartmentofMathematics,HangzhouNormalUniversity,HangzhouCity,ZhejiangProvince310036,P.R.China(Received13January2014;accepted22August2014)DedicatedtoRichardAskeyonhis80thbirthdayInthispaper,weshowhowtodeduceseveralmomen

6、tintegralsbythemethodofq-differenceequation.Inaddition,weobtainseveralgeneralizationsoftransforma-tionalidentitiesbythetechniqueofmomentintegrals.Meanwhile,weobtainsomespecialcasesofbilateralunilateralseriesandtheRogersRamanujanidentitiesasby-products.Moreover,wegivetwom

7、ixedgeneratingfunctionsforgeneralizedRogersSzego¨polynomialsbymomentintegralsandderivetwotransformationalidentitiesbysymmetry.Atlast,atrilineargeneratingfunctionforgeneralizedRogersSzego¨polynomialsisgivenbymomentintegrals.Keywords:momentintegral;generatingfunction;q-dif

8、ferenceequation;RogersSzego¨polynomial;RogersRamanujanidentityMSC(2010)Classification:05A30;11B65;33C45;