求解某些特殊序列發(fā)生函數(shù)的自動化方法.pdf

1、大連理工大學碩士學位論文求解某些特殊序列發(fā)生函數(shù)的自動化方法姓名：王偉平申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：王天明20050601AbstractInthethesis，algorithmsforvcrifyingsomespecialcombinatorialidentitiesandcomputingthegeneratingfunctionsofsomespecialsequencesarestudiedThemaincon

2、tentsofthisthesiscallbesummarizedasfollows：Chapter1describestheevolutionoftheprooftheoryofcombinatorialidentitiesChapter2isaboutthefundamentaltheoryoftheautomaticapproachtocombinatorialidentities，thatis，holonomicfunction

3、sandnoncomm_11tativeoperatoralgebrasBecausethepresentZeilbergeralgorithmrequiresalotofmemorySOthatsomeidentities，suchasDixon’Sidentit：LcannotbeverifiedsuccessfullywegeneralizetheEuclideanalgorithmtothenoneommutativeopera

4、toralgebraC(晶，甌，n，k)inChapter3，andestablishtheeliminationinthenoncommutativecontextBytheuseoftheeliminationinsteadofSylvester’sdialyticelimination，wemodifytheZeilbergeralgorithmSOthatterminatinghypergeometricidentities(b

5、inomialcoefficientsidentities)canbeverifiedautomaticallyBesides，withtheMapleprogrambasedonthemodifiedalgorithm，wehaveproventheidentitiesin[26】，includingSaalschutz’Sidentity，theVandermondcChuconvolutionformula，andDixon’Si

6、dentity，and196identitiesinf101Moreover，withtheWumethod，weconstructthewayofeliminatingseveralvariablesanddevelopanautomaticapproachtoprovingterminatinghypergeomctricidentitiesofseveralvariablesAttheendofthischapter，weintr

7、oducethemainresultsinc(Dx，D“，z，Y)anddiscusstheproblemofverifyingtheidentitieswithtileintegralsignBasedOllthediscussionofChapter3，inChapter4，Weconsiderthegeneratingfunctionsasspecialidentitieswhichcontaincontinuousvariabl

8、esaswellasdiscreteones，andestablishalgorithmsforcomputingthegeneratingfunctionsofsomespecialsequencesInthischapter，wefirstgivethealgorithmforcomputingtheordinarypowerseriesgeneratingfunctionsandtheexponentialgeneratingfu

9、nctionsBytheuseofthisalgorithm，wecomputethegeneratingfunctionsofsomeorthogonalpolynomialsandsomespecialcombinatorialsequencesNext，westudythemethodofcomputing2variableordinarypowerseriesgeneratingfunctionsandmixedtypegene

10、ratingfunctionswiththeapproachtoeliminatingseveralvariablesinthenoncommutativecontextdevelopedinChapter3Andatlast，wegeneralizeourdiscussiontothegeneratingfunctionswithgeneralformsKeywords：Combinatorialidentity；Generating