TraditionalForm Reference Information
TraditionalForm Reference Information
TraditionalForm differs from StandardForm, the default format for input and output. It is important to understand that TraditionalForm expressions cannot always be provided as unambiguous input to the Wolfram System. Therefore, while StandardForm is an input format and an output format, TraditionalForm is primarily intended as an output format.
In general, the TraditionalForm representation of a mathematical function differs from its StandardForm representation in two ways: function arguments are enclosed in parentheses rather than square brackets, and one-character variable and function names are set in italics rather than plain text.
In addition to these general differences, TraditionalForm transforms a large group of expressions into their conventionally used mathematical notation. A table listing these expressions and their special TraditionalForm representations appears later in this tutorial.
This displays a mathematical function that does not have a special notation; the input is in StandardForm and the output is in TraditionalForm:
Here is an example of a function that has its own special TraditionalForm notation:
The TraditionalForm representation of matrices is shown here:
The TraditionalForm representations of the Wolfram System functions and commands distinct from conventional mathematics use square brackets, as in StandardForm.
The following tables list the expressions that have their own specific TraditionalForm representations. Entries marked with a star (⋆) contain hidden information (using TagBox or InterpretationBox constructs or specially designed characters) and may not be suitable for unambiguous input.
StandardForm | TraditionalForm | |
Abs[z] | ![]() | ⋆ |
Arg[z] | ![]() | |
Ceiling[z] | ![]() | |
Conjugate[z] | ![]() | * |
Floor[z] | ![]() | |
FractionalPart[x] | ![]() | |
Max[z] | ![]() | |
Min[z] | ![]() | |
Sign[z] | ![]() |
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 | ![]() |
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] | ![]() | ⋆ |
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}] | ![]() | ⋆ |
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] | ![]() | ⋆ |
StandardForm | TraditionalForm | |
LerchPhi[z,s,a] | ![]() | ⋆ |
PolyLog[n,z] | ![]() | ⋆ |
PolyLog[n,p,z] | ![]() | ⋆ |
RiemannSiegelTheta[t] | ![]() | ⋆ |
RiemannSiegelZ[t] | ![]() | ⋆ |
StieltjesGamma[z] | ![]() | ⋆ |
Zeta[s] | ![]() | ⋆ |
Zeta[s,a] | ![]() | ⋆ |
StandardForm | TraditionalForm | |
AiryAi[z] | ![]() | |
AiryAiPrime[z] | ![]() | |
AiryBi[z] | ![]() | |
AiryBiPrime[z] | ![]() | |
AngerJ[ν,x] | ![]() | * |
AngerJ[ν,μ,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[ν,z] | ![]() | ⋆ |
StruveL[ν,z] | ![]() | ⋆ |
WeberE[ν,x] | ![]() | * |
WeberE[ν,μ,x] | ![]() | * |
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,θ,ϕ] | ![]() | ⋆ |
StandardForm | TraditionalForm | |
InverseErf[z0,s] | ![]() | |
InverseFunction[f] | ![]() | ⋆ |
ProductLog[z] | ![]() | ⋆ |
ProductLog[k,z] | ![]() | ⋆ |
StandardForm | TraditionalForm | |
EllipticE[m] | ![]() | |
EllipticE[ϕ,m] | ![]() | ⋆ |
EllipticF[ϕ,m] | ![]() | ⋆ |
EllipticK[m] | ![]() | |
EllipticNomeQ[m] | ![]() | ⋆ |
EllipticPi[n,m] | ![]() | ⋆ |
EllipticPi[n,ϕ,m] | ![]() | ⋆ |
JacobiZeta[ϕ,m] | ![]() | ⋆ |
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[τ] | ![]() | ⋆ |
ModularLambda[τ] | ![]() | ⋆ |
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}] | ![]() | ⋆ |
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,…] | ![]() | * |
StandardForm | TraditionalForm | |
Det[A] | ![]() | ⋆ |
Inverse[A] | ![]() | |
Transpose[A] | ![]() |
StandardForm | TraditionalForm | |
And[p1,p2,…] | ![]() | |
Implies[a,b] | ![]() | ⋆ |
Nand[p1,p2,…] | ![]() | |
Nor[p1,p2,…] | ![]() | |
Not[p] | ![]() | |
Or[p1,p2,…] | ![]() | |
Xor[p1,p2,…] | ![]() |
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}] | ![]() | ⋆ |
StandardForm | TraditionalForm | |
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,...}] | ![]() |
StandardForm | TraditionalForm | |
Cyclotomic[n,z] | ![]() | ⋆ |
PolynomialMod[poly,m] | ![]() | ⋆ |
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] | ![]() | * |