积分.级数和乘积表I.S.GRADSHTEYN（第6版）

　　This completely reset sixth edition of Gradshteyn and Ryzhik is a corrected and expanded version of the previous edition. The book was completely reset in order to add more material and to enhance the visual appearance of the material. To preserve compatibility with the previous edition， the original numbering system for entries has been retained. New entries and sections have been inserted in a manner consistent with the original scheme. Whenever possible， new entries and corrections have been checked by means of symbolic computation. The diverse ways in which corrections have been contributed have made it impossible to attribute them to reference sources that are accessible to users of this book. However， as in previous editions， our indebtedness to these contributors is shown in the form of an acknowledgment list on page xxiii. This list gives the names of those who have written to ns directly' sending corrections and suggestions for addenda， and added to it are the names of those who have published errata in Mathematics of Computation. Certain individuals must be singled out for special thanks due to their significant contributions： Professors H. van Haeringen and L; P. Kok of The Netherlands and Dr. K. S. Ko1big have contributed new material， corrections， and suggestions for new material.

暂缺《积分.级数和乘积表I.S.GRADSHTEYN（第6版）》作者简介

PrefacetotheSixthEdition
Acknowledgments
Theorderofpresentationoftheformulas
Useofthetables
Specialfunctions
Notation
Noteonthebibliographicreferences
Introduction
0.1Finitesums
0.2Numericalseriesandinfiniteproducts
0.3Functionalseries
0.4Certainformulasfromdifferentialcalculus
1.1PowerofBinomials
1.2TheExponentialFunction
1.3-1.4TrigonometricandHyperbolicFunctions
1.5
1.6TheInverseTrigonometricandHyperbolicFunctions
2IndefiniteIntegralsofElementaryFunctions
2.0Introduction
2.1Rationalfunctions
2.2Algebraicfunctions
2.3TheExponentialFunction
2.4HyperbolicFunctions
2.5-2.6TrigonometricFunctions
2.7LogarithmsandInverse-HyperbolicFunctions
2.8InverseTrigonometricFunctions
3-4DefiniteIntegralsofElementaryFunctions
3.0Introduction
3.1-3.2PowerandAlgebraicFunctions
3.3-3.4ExponentialFunctions
3.5HyperbolicFunctions
3.6-4.1TrigonometricFunctions
4.2-4.4LogarithmicFunctions
4.5InverseTrigonometricFunctions
4.6MultipleIntegrals
5IndefiniteIntegralsofSpecialFunctions
5.1EllipticIntegralsandFunctions
5.2TheExponentialIntegralFunction
5.3TheSineIntegralandtheCosineIntegral
5.4TheProbabilityIntegralandFresnelIntegrals
5.5BesselFunctions
6-7DefiniteIntegralsofSpecialFunctions
6.1EllipticIntegralsandFunctions
6.2-6.3TheExponentialIntegralFunctionandFunctionsGeneratedbyIt
6.4TheGammaFunctionandFunctionsGeneratedbyIt
6.5-6.7BesselFunctions
6.8FunctionsGeneratedbyBesselFunctions
6.9MathieuFunctions
7.1-7.2AssociatedLegendreFunctions
7.3-7.4OrthogonalPolynomials
7.5HypergeometricFunctions
7.6ConfluentHypergeometricFunctions
7.7ParabolicCylinderFunctions
7.8Meijer'sandMacRobert'sFunctions(GandE)
8-9SpecialFunctions
8.1Ellipticintegralsandfunctions
8.2TheExponentialIntegralFunctionandFunctionsGeneratedbyIt
8.3Euler'sIntegralsoftheFirstandSecondKinds
8.4-8.5BesselFunctionsandFunctionsAssociatedwithThem
8.6MathieuFunctions
8.7-8.8AssociatedLegendreFunctions
8.9OrthogonalPolynomials
9.1HypergeometricFunctions
9.2ConfluentHypergeometricFunctions
9.3Meijer'sG-Function
9.4MacRobert'sE-Function
9.5Riemann'sZetaFunctions(z,q),and(z),andtheFunctions(z,s,v)and(s)
9.6Bernoullinumbersandpolynomials,Eulernumbers
9.7Constants
10VectorFieldTheory
10.1-10.8Vectors,VectorOperators,andIntegralTheorems
11AlgebraicInequalities
11.1-11.:3GeneralAlgebraicInequalities
12IntegralInequalities
12.11Meanvaluetheorems
12.21Differentiationofdefiniteintegralcontainingaparameter
12.31Integralinequalities
12.41ConvexityandJensen'sinequality
12.51Fourierseriesandrelatedinequalities
13Matricesandrelatedresults
13.11-13.12Specialmatrices
13.21Quadraticforms
13.31Differentiationofmatrices
13.41Thematrixexponential
14Determinants
14.11Expansionofsecond-andthird-orderdeterminants
14.12Basicproperties
14.13Minorsandcofactorsofadeterminant
14.14Principalminors
14.15Laplaceexpansionofadeterminant
14.16Jacobi'stheorem
14.17Hadamard'stheorem
14.18Hadamard'sinequality
14.21Cramer'srule
14.31Somespecialdeterminants
15Norms
15.1-15.9VectorNorms
15.11Generalproperties
15.21Principalvectornorms
15.31Matrixnorms
15.41Principalnaturalnorms
15.51Spectralradiusofasquarematrix
15.61Inequalitiesinvolvingeigenvaluesofmatrices
15.71Inequalitiesforthecharacteristicpolynomial
15.81-15.82Namedtheoremsoneigenvalues
15.91Variationalprinciples
16Ordinarydifferentialequations
16.1-16.9Resultsrelatingtothesolutionofordinarydifferentialequations
16.tlFirst-orderequations
16.21Fundamentalinequalitiesandrelatedresults
16.31First-ordersystems
16.41Somespecialtypesofelementarydifferentialequations
16.51Second-orderequations
16.61-16.62Oscillationandnon-oscillationtheoremsforsecond-orderequations
16.71Tworelatedcomparisontheorems
16.81-16.82Non-oscillatorysolutions
16.91Somegrowthestimatesforsolutionsofsecond-orderequations
16.92Boundednesstheorems
17Fourier,Laplace,andMellinTransforms
17.1-17.4IntegralTransforms
18Thez-transform
18.1-18.3Definition,Bilateral,andUnilateralz-Transforms
References
Supplementalreferences
Functionandconstantindex
Generalindex