The.Art.Of.Computer.Programming.Vol.1.-.Fundamental.Algorithms.(Addison.Wesley).-.Donald.Knuth

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

2、loveniaPhiladelphia,PA,USADoronZeilbergerTempleUniversityPhiladelphia,PA,USAApril27,1997iiContentsForewordviiAQuickStart:::ixIBackground11ProofMachines31.1Evolutionoftheprovinceofhumanthought..............31.2Canonicalandnormalforms.......................71.3Polynomialidentities...............

3、............81.4Proofsbyexample?............................91.5Trigonometricidentities.........................111.6Fibonacciidentities............................121.7Symmetricfunctionidentities......................121.8Ellipticfunctionidentities........................132TighteningtheTarge

4、t172.1Introduction................................172.2Identities..................................212.3Humanandcomputerproofs;anexample................232.4AMathematicasession..........................272.5AMaplesession..............................292.6Whereweareandwhathappensnext...........

5、.......302.7Exercises..................................313TheHypergeometricDatabase333.1Introduction................................333.2Hypergeometricseries...........................343.3Howtoidentifyaseriesashypergeometric...............353.4Softwarethatidenti¯eshypergeometricseries........

6、......39ivCONTENTS3.5Someentriesinthehypergeometricdatabase..............423.6Usingthedatabase............................443.7Istherereallyahypergeometricdatabase?...............483.8Exercises..................................50IITheFiveBasicAlgorithms534SisterCeline'sMethod554.1Introduction.

7、...............................554.2SisterMaryCelineFasenmyer......................574.3SisterCeline'sgeneralalgorithm.....................584.4TheFundamentalTheorem.......................644.5Multivariateandq"generalizations..........