MATHEMATICA 教程

 数学常数和域 椭圆函数 数值函数 Mathieu 函数 初等函数 广义函数及相关函数 与阶乘相关的函数 矩阵运算 组合函数 逻辑运算 数论 微积分 与 Zeta 函数相关的函数 离散微积分 与超几何函数相关的函数 多项式函数 正交多项式 q 函数 反函数 完整的字母序列表 椭圆积分

Mathematica 函数和命令的 TraditionalForm 表示与使用方括号（例如在 StandardForm 中）的传统数学表示不同.

## 数学常数和域

 StandardForm TraditionalForm Algebraics Booleans Catalan ChampernowneNumber[b] * Complexes EulerGamma Glaisher GoldenRatio Integers Khinchin * Primes Rationals Reals StieltjesGamma[n] * StieltjesGamma[n,a] *

## 数值函数

 StandardForm TraditionalForm Abs[z] Arg[z] Ceiling[z] Conjugate[z] * Floor[z] FractionalPart[x] Max[z] Min[z] Sign[z]

## 初等函数

 StandardForm TraditionalForm ArcCos[z] ArcCosh[z] ArcCot[z] ArcCoth[z] ArcCsc[z] ArcCsch[z] ArcSec[z] ArcSech[z] ArcSin[z] ArcSinh[z] ArcTan[z] ArcTanh[z] Cos[z] Cos[z]p Cosh[z] Cosh[z]p Cot[z] Cot[z]p Coth[z] Coth[z]p Csc[z] Csc[z]p Csch[z] Csch[z]p Log[z] Log[z]^p Log[b,z] Log[b,z]^p Sec[z] Sec[z]p Sech[z] Sech[z]p Sin[z] Sin[z]p Sinh[z] Sinh[z]p Tan[z] Tan[z]p Tanh[z] Tanh[z]p

## 与阶乘相关的函数

 StandardForm TraditionalForm Beta[a,b] Beta[z,a,b] Beta[z0,z1,a,b] Binomial[n,m] Gamma[z] Gamma[a,z] Gamma[a,z1,z2] GammaRegularized[a,z] GammaRegularized[a,z0,z1] InverseBetaRegularized[s,a,b] InverseBetaRegularized[z0,s,a,b] LogGamma[z] Multinomial[n1,n2,...,nk] Pochhammer[a,n] PolyGamma[z] PolyGamma[n,z]

## 组合函数

 StandardForm TraditionalForm BernoulliB[n] BernoulliB[n,z] ClebschGordan[{j1,m1},{j2,m2},{j3,m3}] EulerE[n] EulerE[n,z] Fibonacci[n] Fibonacci[n,z] HarmonicNumber[n] HarmonicNumber[n,r] PartitionsP[z] PartitionsQ[z] Signature[e1,e2,...] SixJSymbol[{j1,j2,j3},{j4,j5,j6}] StirlingS1[n,m] StirlingS2[n,m] ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}]

## 数论

 StandardForm TraditionalForm ArithmeticGeometricMean[a,b] CarmichaelLambda[n] DivisorSigma[k,n] EulerPhi[n] GCD[n1,n2,...] JacobiSymbol[n,m] LCM[n1,n2,...] LiouvilleLambda[n] * MangoldtLambda[n] * Mod[m,n] MoebiusMu[n] MultiplicativeOrder[k,n] PowerMod[a,b,n] Prime[n] PrimeNu[n] * PrimeOmega[n] * PrimeZetaP[x] * PrimePi[z] RamanujanTau[n] RiemannR[x] * SquaresR[d,n]

## 与 Zeta 函数相关的函数

 StandardForm TraditionalForm LerchPhi[z,s,a] PolyLog[n,z] PolyLog[n,p,z] RiemannSiegelTheta[t] RiemannSiegelZ[t] StieltjesGamma[z] Zeta[s] Zeta[s,a]

## 与超几何函数相关的函数

 StandardForm TraditionalForm AiryAi[z] AiryAiPrime[z] AiryBi[z] AiryBiPrime[z] AngerJ[,x] * AngerJ[,,x] * AppellF1[a,b1,b2,c,x,y] BesselI[n,z] BesselJ[n,z] BesselK[n,z] BesselY[n,z] CosIntegral[z] CoshIntegral[z] DawsonF[x] * Erf[z] Erf[z0,z1] Erfc[z] Erfi[z] ExpIntegralE[n,z] ExpIntegralEi[z] FresnelC[z] FresnelS[z] Hypergeometric0F1[a,z] Hypergeometric0F1Regularized[a,z] Hypergeometric1F1[a,b,z] Hypergeometric1F1Regularized[a,b,z] Hypergeometric2F1[a,b,c,z] Hypergeometric2F1Regularized[a,b,c,z] HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] HypergeometricU[a,b,z] LegendreQ[n,x] LegendreQ[n,m,x] LegendreQ[n,m,a,z] LogIntegral[z] MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r] SinIntegral[z] SinhIntegral[z] StruveH[,z] StruveL[,z] WeberE[,x] * WeberE[,,x] *

## 正交多项式

 StandardForm TraditionalForm ChebyshevT[n,x] ChebyshevU[n,x] GegenbauerC[n,x] GegenbauerC[n,m,x] HermiteH[n,x] JacobiP[n,a,b,x] LaguerreL[n,x] LaguerreL[n,a,x] LegendreP[n,x] LegendreP[n,m,x] LegendreP[n,m,a,z] SphericalHarmonicY[l,m,,]

## 反函数

 StandardForm TraditionalForm InverseErf[z0,s] InverseFunction[f] ProductLog[z] ProductLog[k,z]

## 椭圆积分

 StandardForm TraditionalForm EllipticE[m] EllipticE[,m] EllipticF[,m] EllipticK[m] EllipticNomeQ[m] EllipticPi[n,m] EllipticPi[n,,m] JacobiZeta[,m]

## 椭圆函数

 StandardForm TraditionalForm DedekindEta[t] EllipticTheta[a,u,q] EllipticThetaPrime[a,u,q] InverseEllipticNomeQ[q] InverseJacobiCD[u,m] InverseJacobiCN[u,m] InverseJacobiCS[u,m] InverseJacobiDC[u,m] InverseJacobiDN[u,m] InverseJacobiDS[u,m] InverseJacobiNC[u,m] InverseJacobiND[u,m] InverseJacobiNS[u,m] InverseJacobiSC[u,m] InverseJacobiSD[u,m] InverseJacobiSN[u,m] InverseWeierstrassP[p,{g2,g3}] JacobiAmplitude[u,m] JacobiCD[u,m] JacobiCN[u,m] JacobiCS[u,m] JacobiDC[u,m] JacobiDN[u,m] JacobiDS[u,m] JacobiNC[u,m] JacobiND[u,m] JacobiNS[u,m] JacobiSC[u,m] JacobiSD[u,m] JacobiSN[u,m] KleinInvariantJ[] ModularLambda[] NevilleThetaC[u,m] NevilleThetaD[u,m] NevilleThetaN[u,m] NevilleThetaS[u,m] WeierstrassP[u,{g2,g3}] WeierstrassPPrime[u,{g2,g3}] WeierstrassSigma[u,{g2,g3}] WeierstrassZeta[u,{g2,g3}]

Mathieu 函数.

## 广义函数及相关函数

 StandardForm TraditionalForm DiracDelta[x1,x2,...] DiscreteDelta[n1,n2,...] HeavisideLambda[x] * HeavisideLambda[x1,x2,...] * HeavisidePi[x] * HeavisidePi[x1,x2,...] * KroneckerDelta[n1,n2,...] UnitBox[x] * UnitBox[x1,x2,...] * UnitStep[x1,x2,...] UnitTriangle[x] * UnitTriangle[x1,x2,...] *

## 逻辑运算

 StandardForm TraditionalForm And[p1,p2,...] Implies[a,b] Nand[p1,p2,...] Nor[p1,p2,...] Not[p] Or[p1,p2,...] Xor[p1,p2,...]

## 微积分

 StandardForm TraditionalForm C[n] D[f[x]] D[f[x],x] D[f[x],{x,2}] D[f[x],{x,n}] Dt[f[x]] Dt[f[x],x] Dt[f[x],{x,2}] Dt[f[x],{x,n}] Derivative[1][f] Derivative[2][f] Derivative[d1,...][f] FourierTransform[expr,t,s] FourierTransform[expr,{t1,t2,...},{s1,s2,...}] Integrate[expr,x] Integrate[expr,x1,y,z] Integrate[expr,{x,a,b}] Integrate[expr,{x,a,b},{y,m,n},{z,p,q}] InverseFourierTransform[expr,s,t] InverseFourierTransform[expr,{s1,s2,...},{t1,t2,...}] InverseLaplaceTransform[expr,s,t] InverseLaplaceTransform[expr,{s1,s2,...},{t1,t2,...}] LaplaceTransform[expr,t,s] LaplaceTransform[expr,{t1,t2,...},{s1,s2,...}] Limit[f[x],x->a] Limit[f[x],x->a,Direction->+1] Limit[f[x],x->a,Direction->-1] O[x] O[x]^n O[x,a] O[x,a]^n Piecewise[{{v1,c1},{v2,c2},...}] Residue[z] Series[f[x],{x,a,0}] Series[f[x],{x,a,1}] Series[Tan[z^(2/3)],{z,0,3}]

## 离散微积分

DifferenceDelta[f,i]*
DifferenceDelta[f,{i,n}]*
DifferenceDelta[f,{i,n,h}]*
DifferenceDelta[f,i,j,...]*
DiscreteRatio[f,i]*
DiscreteRatio[f,{i,n}]*
DiscreteRatio[f,{i,n,h}*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]*
DiscreteShift[f,{i,n,h}]*
DiscreteShift[f,i,j,...]*
InverseZTransform[exp,z,n]
InverseZTransform[exp,{z1,z2,...},{n1,n2,...}]
ZTransform[exp,n,z]
ZTransform[exp,{n1,n2,...},{z1,z2,...}]

## q 函数

 StandardForm TraditionalForm QBinomial[n,m,q] * QFactorial[n,q] * QGamma[z,q] * QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z] * QPochhammer[a,q,n] * QPochhammer[a,q] * QPochhammer[q] * QPolyGamma[z,q] * QPolyGamma[n,z,q] *

Q 函数.

## 完整的字母序列表

Abs[z]
AiryAi[z]
AiryAiPrime[z]
AiryBi[z]
AiryBiPrime[z]
Algebraics
And[p1,p2,...]
AngerJ[,x]*
AngerJ[,,x]*
AppellF1[a,b1,b2,c,x,y]
ArcCos[z]
ArcCosh[z]
ArcCot[z]
ArcCoth[z]
ArcCsc[z]
ArcCsch[z]
ArcSec[z]
ArcSech[z]
ArcSin[z]
ArcSinh[z]
ArcTan[z]
ArcTanh[z]
Arg[z]
ArithmeticGeometricMean[a,b]
BernoulliB[n]
BernoulliB[n,z]
BesselI[n,z]
BesselJ[n,z]
BesselK[n,z]
BesselY[n,z]
Beta[a,b]
Beta[z,a,b]
Beta[z0,z1,a,b]
BetaRegularized[z,a,b]
BetaRegularized[z0,z1,a,b]
Binomial[n,m]
Booleans
C[n]
CarmichaelLambda[n]
Catalan
Ceiling[z]
ChampernowneNumber[b]*
ChebyshevT[n,x]
ChebyshevU[n,x]
ClebschGordan[{j1,m1},{j2,m2},{j3,m3}]
Complexes
Conjugate[z]*
Cos[z]
Cos[z]p
Cosh[z]
Cosh[z]p
CosIntegral[z]
CoshIntegral[z]
Cot[z]
Cot[z]p
Coth[z]
Coth[z]p
Csc[z]
Csc[z]p
Csch[z]
Csch[z]p
Cyclotomic[n,z]
D[f[x]]
D[f[x],x]
D[f[x],{x,2}]
D[f[x],{x,n}]
Dt[f[x]]
Dt[f[x],x]
Dt[f[x],{x,2}]
Dt[f[x],{x,n}]
DawsonF[x]*
DedekindEta[t]
Derivative[1][f]
Derivative[2][f]
Derivative[d1,...][f]
Det[A]
DifferenceDelta[f,i]*
DifferenceDelta[f,{i,n}]*
DifferenceDelta[f,{i,n,h}]*
DifferenceDelta[f,i,j,...]*
DiracDelta[x1,x2,...]
DiscreteDelta[n1,n2,...]
DiscreteRatio[f,i]*
DiscreteRatio[f,{i,n}]*
DiscreteRatio[f,{i,n,h}*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]*
DiscreteShift[f,{i,n,h}]*
DiscreteShift[f,i,j,...]*
DivisorSigma[k,n]
EllipticE[m]
EllipticE[,m]
EllipticF[,m]
EllipticK[m]
EllipticNomeQ[m]
EllipticPi[n,m]
EllipticPi[n,,m]
EllipticTheta[a,u,q]
EllipticThetaPrime[a,u,q]
Erf[z]
Erf[z0,z1]
Erfc[z]
Erfi[z]
EulerE[n]
EulerE[n,z]
EulerGamma
EulerPhi[n]
ExpIntegralE[n,z]
ExpIntegralEi[z]
Fibonacci[n]
Fibonacci[n,z]
Floor[z]
FourierTransform[expr,t,s]
FourierTransform[expr,{t1,t2,...},{s1,s2,...}]
FractionalPart[x]
FresnelC[z]
FresnelS[z]
Gamma[z]
Gamma[a,z]
Gamma[a,z1,z2]
GammaRegularized[a,z]
GammaRegularized[a,z0,z1]
GCD[n1,n2,...]
GegenbauerC[n,x]
GegenbauerC[n,m,x]
Glaisher
GoldenRatio
HarmonicNumber[n]
HarmonicNumber[n,r]
HeavisideLambda[x]*
HeavisideLambda[x1,x2,...]*
HeavisidePi[x]*
HeavisidePi[x1,x2,...]*
HermiteH[n,x]
Hypergeometric0F1[a,z]
Hypergeometric0F1Regularized[a,z]
Hypergeometric1F1[a,b,z]
Hypergeometric1F1Regularized[a,b,z]
Hypergeometric2F1[a,b,c,z]
Hypergeometric2F1Regularized[a,b,c,z]
HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z]
HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z]
HypergeometricU[a,b,z]
Implies[a,b]
Integers
Integrate[expr,x]
Integrate[expr,x1,y,z]
Integrate[expr,{x,a,b}]
Integrate[expr,{x,a,b},{y,m,n},{z,p,q}]
Inverse[A]
InverseBetaRegularized[s,a,b]
InverseBetaRegularized[z0,s,a,b]
InverseEllipticNomeQ[q]
InverseErf[z0,s]
InverseFourierTransform[expr,s,t]
InverseFourierTransform[expr,{s1,s2,...},{t1,t2,...}]
InverseFunction[f]
InverseJacobiCD[u,m]
InverseJacobiCN[u,m]
InverseJacobiCS[u,m]
InverseJacobiDC[u,m]
InverseJacobiDN[u,m]
InverseJacobiDS[u,m]
InverseJacobiNC[u,m]
InverseJacobiND[u,m]
InverseJacobiNS[u,m]
InverseJacobiSC[u,m]
InverseJacobiSD[u,m]
InverseJacobiSN[u,m]
InverseLaplaceTransform[expr,s,t]
InverseLaplaceTransform[expr,{s1,s2,...},{t1,t2,...}]
InverseWeierstrassP[p,{g2,g3}]
InverseZTransform[exp,z,n]
InverseZTransform[exp,{z1,z2,...},{n1,n2,...}]
JacobiAmplitude[u,m]
JacobiCD[u,m]
JacobiCN[u,m]
JacobiCS[u,m]
JacobiDC[u,m]
JacobiDN[u,m]
JacobiDS[u,m]
JacobiNC[u,m]
JacobiND[u,m]
JacobiNS[u,m]
JacobiSC[u,m]
JacobiSD[u,m]
JacobiSN[u,m]
JacobiP[n,a,b,x]
JacobiSymbol[n,m]
JacobiZeta[,m]
Khinchin*
KleinInvariantJ[]
KroneckerDelta[n1,n2,...]
LaguerreL[n,x]
LaguerreL[n,a,x]
LegendreP[n,x]
LegendreP[n,m,x]
LegendreP[n,m,a,z]
LaplaceTransform[expr,t,s]
LaplaceTransform[expr,s,t]
LCM[n1,n2,...]
LegendreQ[n,x]
LegendreQ[n,m,x]
LegendreQ[n,m,a,z]
LerchPhi[z,s,a]
Limit[f[x],x->a]
Limit[f[x],x->a,Direction->+1]
Limit[f[x],x->a,Direction->-1]
LiouvilleLambda[n]*
Log[z]
Log[b,z]
Log[z]^p
Log[b,z]^p
LogGamma[z]
MangoldtLambda[n]*
MathieuCharacteristicA[r,q]
MathieuCharacteristicB[r,q]
Max[z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r]
Min[z]
Mod[m,n]
ModularLambda[]
MoebiusMu[n]
Multinomial[n1,n2,...,nk]
MultiplicativeOrder[k,n]
Nand[p1,p2,...]
NevilleThetaC[u,m]
NevilleThetaN[u,m]
NevilleThetaS[u,m]
Nor[p1,p2,...]
Not[p]
O[x]
O[x]^n
O[x,a]
O[x,a]^n
Or[p1,p2,...]
PartitionsP[z]
PartitionsQ[z]
Piecewise[{{v1,c1},{v2,c2},...}]
Pochhammer[a,n]
PolyGamma[z]
PolyGamma[n,z]
PolyLog[,z]
PolyLog[,p,z]
PolynomialMod[poly,m]
PowerMod[a,b,n]
Prime[n]
PrimeOmega[n]*
PrimePi[z]
PrimeZetaP[x]*
Primes
ProductLog[z]
ProductLog[k,z]
QBinomial[n,m,q]*
QFactorial[n,q]*
QGamma[z,q]*
QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z]*
QPochhammer[a,q,n]*
QPochhammer[a,q]*
QPochhammer[q]*
QPolyGamma[z,q]*
QPolyGamma[n,z,q]*
RamanujanTau[n]
Rationals
Reals
Residue[z]
RiemannR[x]*
RiemannSiegelTheta[t]
RiemannSiegelZ[t]
Sec[z]
Sec[z]p
Sech[z]
Sech[z]p
Series[f[x],{x,a,0}]
Series[f[x],{x,a,1}]
Series[Tan[z^(2/3)],{z,0,3}]
Sign[z]
Signature[e1,e2,...]
Sin[z]
Sin[z]p
Sinh[z]
Sinh[z]p
SinIntegral[z]
SinhIntegral[z]
SixJSymbol[{j1,j2,j3},{j4,j5,j6}]
SphericalHarmonicY[l,m,,]
SquaresR[d,n]*
StieltjesGamma[n]
StieltjesGamma[n,a]*
StirlingS1[n,m]
StirlingS2[n,m]
StruveH[,z]
StruveL[,z]
Tan[z]
Tan[z]p
Tanh[z]
Tanh[z]p
ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}]
Transpose[A]
UnitBox[x]*
UnitBox[x1,x2,...]*
UnitStep[x1,x2,...]
UnitTriangle[x]*
UnitTriangle[x1,x2,...]*
WeberE[,x]*
WeberE[,,x]*
WeierstrassP[u,{g2,g3}]
WeierstrassPPrime[u,{g2,g3}]
WeierstrassSigma[u,{g2,g3}]
WeierstrassZeta[u,{g2,g3}]
Xor[p1,p2,...]
Zeta[s]
Zeta[s,a]
ZTransform[exp,n,z]
ZTransform[exp,{n1,n2,...},{z1,z2,...}]

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