MATHEMATICA TUTORIAL

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 Mathematica. 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.
In[1]:=
Click for copyable input
Out[1]//TraditionalForm=
Here is an example of a function that has its own special TraditionalForm notation.
In[2]:=
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Out[2]//TraditionalForm=
The TraditionalForm representation of matrices is shown here.
In[3]:=
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Out[3]//TraditionalForm=

The TraditionalForm representations of Mathematica functions and commands distinct from conventional mathematics use square brackets, as in StandardForm.

Here is the TraditionalForm representation of the Mathematica function Plot.
In[4]:=
Click for copyable input
Out[4]//TraditionalForm=

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

Zeta-related functions.

Hypergeometric-Related Functions

StandardFormTraditionalForm
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]*

Hypergeometric-related functions.

Orthogonal Polynomials

Orthogonal polynomials.

Inverse Functions

Inverse functions.

Elliptic Integrals

Elliptic integrals.

Elliptic Functions

Elliptic functions.

Mathieu Functions

Mathieu functions.

Generalized and Related Functions

StandardFormTraditionalForm
DiracDelta[x1,x2,...]
DiscreteDelta[n1,n2,...]
HeavisideLambda[x]*
HeavisideLambda[x1,x2,...]*
HeavisidePi[x]TemplateBox[{x}, HeavisidePiSeq]*
HeavisidePi[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, HeavisidePiSeq]*
KroneckerDelta[n1,n2,...]
UnitBox[x]TemplateBox[{x}, UnitBoxSeq]*
UnitBox[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, UnitBoxSeq]*
UnitStep[x1,x2,...]
UnitTriangle[x]TemplateBox[{x}, UnitTriangleSeq]*
UnitTriangle[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, UnitTriangleSeq]*

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}]TemplateBox[{f, i, n}, DiscreteRatio3]*
DiscreteRatio[f,{i,n,h}TemplateBox[{f, i, n, h}, DiscreteRatio4]*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]TemplateBox[{f, i, n}, DiscreteShift3]*
DiscreteShift[f,{i,n,h}]TemplateBox[{f, i, n, h}, DiscreteShift4]*
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]TemplateBox[{n, m, q}, QBinomial]*
QFactorial[n,q]TemplateBox[{n, q}, QFactorial]*
QGamma[z,q]TemplateBox[{z, q}, QGamma]*
QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z]TemplateBox[{{{a, _, 1}, ,, ..., ,, {a, _, t}}, {{b, _, 1}, ,, ..., ,, {b, _, s}}, q, z, 2, 2}, QHypergeometricPFQSeq]*
QPochhammer[a,q,n]TemplateBox[{a, q, n}, QPochhammer]*
QPochhammer[a,q]TemplateBox[{a, q}, QPochhammer2]*
QPochhammer[q]TemplateBox[{q, q}, QPochhammer2]*
QPolyGamma[z,q]TemplateBox[{0, z, q}, QPolyGamma3]*
QPolyGamma[n,z,q]TemplateBox[{n, z, q}, QPolyGamma3]*

Q functions.

Complete Alphabetical Listing

StandardFormTraditionalForm
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]TemplateBox[{z}, Conjugate]*
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}]TemplateBox[{f, i, n}, DifferenceDelta3]*
DifferenceDelta[f,{i,n,h}]*
DifferenceDelta[f,i,j,...]*
DiracDelta[x1,x2,...]
DiscreteDelta[n1,n2,...]
DiscreteRatio[f,i]*
DiscreteRatio[f,{i,n}]TemplateBox[{f, i, n}, DiscreteRatio3]*
DiscreteRatio[f,{i,n,h}TemplateBox[{f, i, n, h}, DiscreteRatio4]*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]TemplateBox[{f, i, n}, DiscreteShift3]*
DiscreteShift[f,{i,n,h}]TemplateBox[{f, i, n, h}, DiscreteShift4]*
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]TemplateBox[{x}, HeavisidePiSeq]*
HeavisidePi[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, HeavisidePiSeq]*
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]TemplateBox[{n}, LiouvilleLambda]*
Log[z]
Log[b,z]
Log[z]^p
Log[b,z]^p
LogGamma[z]
LogIntegral[z]
MangoldtLambda[n]TemplateBox[{n}, MangoldtLambda]*
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]
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[,z]
PolyLog[,p,z]
PolynomialMod[poly,m]
PowerMod[a,b,n]
Prime[n]
PrimeNu[n]TemplateBox[{x}, PrimeNu]*
PrimeOmega[n]TemplateBox[{n}, PrimeOmega]*
PrimePi[z]
PrimeZetaP[x]*
Primes
ProductLog[z]
ProductLog[k,z]
QBinomial[n,m,q]TemplateBox[{n, m, q}, QBinomial]*
QFactorial[n,q]TemplateBox[{n, q}, QFactorial]*
QGamma[z,q]TemplateBox[{z, q}, QGamma]*
QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z]TemplateBox[{{{a, _, 1}, ,, ..., ,, {a, _, t}}, {{b, _, 1}, ,, ..., ,, {b, _, s}}, q, z, 2, 2}, QHypergeometricPFQSeq]*
QPochhammer[a,q,n]TemplateBox[{a, q, n}, QPochhammer]*
QPochhammer[a,q]TemplateBox[{a, q}, QPochhammer2]*
QPochhammer[q]TemplateBox[{q, q}, QPochhammer2]*
QPolyGamma[z,q]TemplateBox[{0, z, q}, QPolyGamma3]*
QPolyGamma[n,z,q]TemplateBox[{n, z, q}, QPolyGamma3]*
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]TemplateBox[{x}, UnitBoxSeq]*
UnitBox[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, UnitBoxSeq]*
UnitStep[x1,x2,...]
UnitTriangle[x]TemplateBox[{x}, UnitTriangleSeq]*
UnitTriangle[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, UnitTriangleSeq]*
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,...}]

Complete alphabetical listing.

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