The Art of Computer Programming

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1、Thispageintentionallyleftblank[50]Developcomputerprogramsforsimplifyingsumsthatinvolvebinomialcoe±cients.Exercise1.2.6.63inTheArtofComputerProgramming,Volume1:FundamentalAlgorithmsbyDonaldE.Knuth,AddisonWesley,Reading,Massachusetts,1968.A=BMarkoPetkov·sek

2、HerbertS.WilfUniversityofLjubljanaUniversityofPennsylvaniaLjubljana,SloveniaPhiladelphia,PA,USADoronZeilbergerTempleUniversityPhiladelphia,PA,USAApril27,1997iiContentsForewordviiAQuickStart:::ixIBackground11ProofMachines31.1Evolutionoftheprovinceofhumanth

3、ought..............31.2Canonicalandnormalforms.......................71.3Polynomialidentities...........................81.4Proofsbyexample?............................91.5Trigonometricidentities.........................111.6Fibonacciidentities...........

4、.................121.7Symmetricfunctionidentities......................121.8Ellipticfunctionidentities........................132TighteningtheTarget172.1Introduction................................172.2Identities..................................212.3Huma

5、nandcomputerproofs;anexample................232.4AMathematicasession..........................272.5AMaplesession..............................292.6Whereweareandwhathappensnext..................302.7Exercises..................................313TheHypergeo

6、metricDatabase333.1Introduction................................333.2Hypergeometricseries...........................343.3Howtoidentifyaseriesashypergeometric...............353.4Softwarethatidenti¯eshypergeometricseries..............39ivCONTENTS3.5Someentri

7、esinthehypergeometricdatabase..............423.6Usingthedatabase............................443.7Istherereallyahypergeometricdatabase?...............483.8Exercises..................................50IITheFiveBasicAlgorithms534SisterCeline'sMethod554.1Intr

8、oduction................................554.2SisterMaryCelineFasenmyer......................574.3SisterCeline'sgeneralalgorithm.....................584.4TheFundamentalTheorem.......................644.5Multivariatea