基本超幾何級(jí)數(shù)的算子方法、Cauchy方法與反演技巧.pdf

1、大連理工大學(xué)博士學(xué)位論文基本超幾何級(jí)數(shù)的算子方法、Cauchy方法與反演技巧姓名：張彩環(huán)申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：王軍20080601TheOperatorMethod，CauchyMethodandInversionTechniqueforBasicHypergeometricSeriesAbstractBasichypergeometricseries(alsocalledqseries)playsallimport

2、antandspecialroleincombinatorialanalysis，specialfunctionsandnumbertheoryandiswidelyappliedinstatisticsandphysicsetcThemaincontentofthisthesisistofindandprovesomesummationandtransformationformulaeofbasichypergeometricseri

3、esbythemodifiedCauchymethod，operatormethodandinversiontechniques，whichincludemanywellknownresultsasspecialcases，forexample，g—Saalschfitzsummationformula，Bailey’S6幽summationformula，nonterminating％舌sontransformationformula

4、andRogersRamanujanidentitiesetcThethesisconsistsoffourchapters‘InChapter1，wefirstlookbackthehistoryofhypergeometricseriesandbasicpergeometricseries，andthenintroducesomenecessaryconceptsandnotationsChapter2contributestheC

5、auchymethodViageneralizingtheCauchymethodweobtainanewmethod，calledthemodifiedCauchymethodBymeansofthismethodweestablishtwobilateral3咖and4譏seriessummationformulae，twofourtermsummationandtransformationformulaeforunilateral

6、3≯2seriesandbilateral3矽3一series，andtwofivetermsummationandtransformationformulaeforunilateral3≯2一seriesandbilateral3妒3series，Whichcontainmanyknownresultsastheirspecialcases，suchasnon—terminatingq—Saalschfitzsummationform

7、ula，Bilateral6譏seriessummationformulaofBaileynonterminatingWatsontransformationformulaandsometransformationsof3≯2seriesetcChapter3contributestheoperatormethodByusingthismethodweobtaintwogeneralizedtransformationformulaeo

8、fqintegralform，twoidentitiesofbasichypergeometricseries，aswellasformalextensionsforqPfaffSaalschiitzformula，qChuVandermondeidentityandathreetermtransformationformulaof3≯2一seriesInchapter4，bytheinversiontechniqueandtheser

9、iesrearrangement，wefindtwokindsoftransformationformulaeofthebasichypergeometricseriesOneofthemcontainsaspecialcaseofqDougallsummationformula，theotherincludesthefamousRogersRalnanujanidentitiesasspecialCasesKeywords：Basic