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.
Here is the TraditionalForm representation of the Wolfram System function Plot:
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.
Mathematical Constants and Domains
Mathematical constants and domains.
Numerical Functions
Numerical functions.
Elementary Functions
StandardFormTraditionalForm
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
Elementary functions.
Factorial-Related Functions
StandardFormTraditionalForm
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]
Factorial-related functions.
Combinatorial Functions
StandardFormTraditionalForm
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}]
Combinatorial functions.
Number Theory
Number theory.
Zeta-Related Functions
StandardFormTraditionalForm
LerchPhi[z,s,a]
PolyLog[n,z]
PolyLog[n,p,z]
RiemannSiegelTheta[t]
RiemannSiegelZ[t]
StieltjesGamma[z]
Zeta[s]
Zeta[s,a]
Zeta-related functions.
Hypergeometric-Related Functions
StandardFormTraditionalForm
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]*
Hypergeometric-related functions.
Orthogonal Polynomials
StandardFormTraditionalForm
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]
Orthogonal polynomials.
Inverse Functions
Inverse functions.
Elliptic Integrals
Elliptic integrals.
Elliptic Functions
StandardFormTraditionalForm
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}]
Elliptic functions.
Mathieu Functions
Mathieu functions.
Generalized and Related Functions
StandardFormTraditionalForm
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,]*
Generalized and related functions.
Matrix Operations
Matrix operations.
Logical Operations
StandardFormTraditionalForm
And[p1,p2,]
Implies[a,b]
Nand[p1,p2,]
Nor[p1,p2,]
Not[p]
Or[p1,p2,]
Xor[p1,p2,]
Logical operations.
Calculus
StandardFormTraditionalForm
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}]
Calculus.
Discrete Calculus
StandardFormTraditionalForm
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,...}]
Discrete calculus.
Polynomial Functions
Polynomial functions.
q Functions
StandardFormTraditionalForm
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 functions.
Complete Alphabetical Listing
StandardFormTraditionalForm
Abs[z]
AiryAi[z]
AiryAiPrime[z]
AiryBi[z]
AiryBiPrime[z]
Algebraics
And[p1,p2,]
AngerJ[ν,x]*
AngerJ[ν,μ,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[ϕ,m]
EllipticF[ϕ,m]
EllipticK[m]
EllipticNomeQ[m]
EllipticPi[n,m]
EllipticPi[n,ϕ,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[ϕ,m]
Khinchin*
KleinInvariantJ[τ]
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]
LogIntegral[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[τ]
MoebiusMu[n]
Multinomial[n1,n2,,nk]
MultiplicativeOrder[k,n]
Nand[p1,p2,]
NevilleThetaC[u,m]
NevilleThetaD[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[ν,z]
PolyLog[ν,p,z]
PolynomialMod[poly,m]
PowerMod[a,b,n]
Prime[n]
PrimeNu[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,θ,ϕ]
SquaresR[d,n]*
StieltjesGamma[n]
StieltjesGamma[n,a]*
StirlingS1[n,m]
StirlingS2[n,m]
StruveH[ν,z]
StruveL[ν,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[ν,x]*
WeberE[ν,μ,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,}]
Complete alphabetical listing.