基本超幾何級數(shù)及其應(yīng)用.pdf

1、大連理工大學(xué)碩士學(xué)位論文基本超幾何級數(shù)及其應(yīng)用姓名：劉俊同申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：王天明20060601基本超幾何級數(shù)及其應(yīng)用BasicHypergeometricSeriesanditsApplicationsAbstractInthethe8i8，theb撕icknowledseofthebasichype。geometricseTie8，80meresultsofthef沁gersR鋤anujantypeiden

2、titiesanditsapplicationsinnumbertheoryarestudjedThemaincontent8ofthi8thesiscanbesummarizedasb110岬8：IⅡChapter1，weintroducethedevelopmentofthebasichypergeometricseriesInChapter2，weintroducethebasicknawledgeoftheba8ichyperg

3、eometricseries，includingbasicconcept8，80mesummationformula8，tran8formatbn矗Ⅱnllas，etcInChapter3，bymeansofCarlitziIlver8ionformul私aJldatran8formationofbasjchypergeometric8erje8obt越nedbyChu，wegivenewproo缸f曲seVera】RogersRa腳a

4、nujantypeidentitie8Furthermore，somenewRoger8ramanujantypeidentitiesareobtalnedbyatransformationofbasichypergeometricseriesInChapter4，bysomeimportantsumInationformul船，、Veprove80mere8ult8of叫mbertheory，sucllasJacobit、Vosqua

5、reHumberstheoremaIldLagrangefoursquarenumber8theoremTnaddition，byutjlizingJacobjtwosquarenumber8theoremandLa鏟a1唱efoursquarenumb日stheoremand80nlethetafunctioniden“ties，wealsoprovetheknownresult8ofHumbertheofy：twotrjangula

6、rnllmbertheorem，fourtrja“gularnumbertheorem，andthemlmberofrepre8entatioIl8ofapositiveintegerbyvariousquadraticf曲msintermsofdivisorfunctionsKeywordsBasichype。geometricseries；seriestransformation；Rogers—Ramanujantypeiden七i