歐拉的級數(shù)理論研究.pdf

1、西北大學碩士學位論文歐拉的級數(shù)理論研究姓名：金英姬申請學位級別：碩士專業(yè)：科學技術(shù)史指導教師：曲安京20080610西北大學碩士學位論文StudyonEuler’sTheoryoftheSeriesAbstractInfimteserieshaSsubs伽tiVedeVelopedsincethecreationofthecalculushlⅡle18廿lcentu巧，thefonnalizedViewtookadominatcplac

2、eiIltlletheor)，ofinfiIliteseriesDuring廿lisperiod，sornespecialt)，pesofseriesemerged，suchastlleaSyrnptoticseries，tllerecurrentseries，thecontimled劬ctionsaIldsoonThenewt)，pesofseries、Ⅳerebeyondtlleoriginalmeo哆a11dleadmem劬ema

3、tici鋤samorcf0mlalizedtreatnlentofthemEuler，弱arepresentitiVeofmem，genaralizedⅡ圮earlyseriestlleo巧bymeformalization印proachf如mmany嬲pectsEulerdeVelopedamorefomlal印proachwmch薩neralizedmeearlytlleoryHe艄lsfonlledtlleiⅢi11iteseri

4、es矗Dmaordilla巧calculationtoolint0觚imponaIlts州ect鋤ddeepenedtlle印plicationofseriest0anewleVel，w11ichlaidmef0Ⅲldationforthe矗m鵬developmentoftheseriesthe0巧刪sp印erdiscussesEuler’soriginalworkSonmeor)r0fmeseries，iemehannonicseri

5、es，t：heB嬲elproblem，tlleZeta如nction，tllesummationofdive唱entseries，tllen硼【lericalapproximation，tllesolutionofdi腩rentialequations，metrigonometricseries鋤dthecontinuedfactionsBaSedonthecare如la11dmorougllstudyofEuler’sbrillian

6、tmemodsandide鎬，thep印erconcludestl讎Euler’skeymemod、Ⅳ_hendealingwitIltIleseriestheoryisfo咖alization觚dtllatthecoreofEuler’swhole、vorkintllisfieldisthe翻HnmationofⅡleseriesKeywords：Euler；irIfiIliteseries；formalization；suI姍ati