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Mathematical Functions

Logarithms and special functions

Use a wide variety of mathematical functions in your computations — from basic functions, such as sine and cosine functions, to special functions, such as the Riemann zeta function and Bessel functions.


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catalanCatalan constant
eulergammaEuler-Mascheroni constant


logNatural logarithm of entries of symbolic matrix
log10Log base 10 of symbolic input
log2Base-2 logarithm of symbolic input

Polylogarithms and Zeta Function

dilogDilogarithm function
hurwitzZetaHurwitz zeta function
psiDigamma function
zetaRiemann zeta function

Trigonometric Functions

sinSymbolic sine function
sincNormalized sinc function
cosSymbolic cosine function
tanSymbolic tangent function
cotSymbolic cotangent function
secSymbolic secant function
cscSymbolic cosecant function

Inverse Trigonometric Functions

asinSymbolic inverse sine function
acosSymbolic inverse cosine function
atanSymbolic inverse tangent
acotSymbolic inverse cotangent function
asecSymbolic inverse secant function
acscSymbolic inverse cosecant function

Hyperbolic Functions

sinhSymbolic hyperbolic sine function
coshSymbolic hyperbolic cosine function
tanhSymbolic hyperbolic tangent function
cothSymbolic hyperbolic cotangent function
sechSymbolic hyperbolic secant function
cschSymbolic hyperbolic cosecant function

Inverse Hyperbolic Functions

asinhSymbolic inverse hyperbolic sine function
acoshSymbolic inverse hyperbolic cosine function
atanhSymbolic inverse hyperbolic tangent function
acothSymbolic inverse hyperbolic cotangent function
asechSymbolic inverse hyperbolic secant function
acschSymbolic inverse hyperbolic cosecant function
absSymbolic absolute value (complex modulus or magnitude)
angleSymbolic polar angle
atan2Symbolic four-quadrant inverse tangent
conjComplex conjugate of symbolic input
imagImaginary part of complex number
nthrootNth root of symbolic numbers
realReal part of complex number
signSign of real or complex value
signImSign of the imaginary part of complex number

Gamma Functions

betaBeta function
factorialFactorial of symbolic input
gammaGamma function
gammalnLogarithmic gamma function
igammaIncomplete gamma function
nchoosekBinomial coefficient
pochhammerPochhammer symbol

Error Functions

dawsonDawson integral
erfError function
erfcComplementary error function
erfcinvInverse complementary error function
erfiImaginary error function
erfinvInverse error function
fresnelcFresnel cosine integral function
fresnelsFresnel sine integral function

Trigonometric Integrals

coshintHyperbolic cosine integral function
cosintCosine integral function
eiOne-argument exponential integral function
expintExponential integral function
eulergammaEuler-Mascheroni constant
logintLogarithmic integral function
sinhintHyperbolic sine integral function
sinintSine integral function
ssinintShifted sine integral function

Elliptic Integrals

ellipkeComplete elliptic integrals of the first and second kinds
ellipticCEComplementary complete elliptic integral of the second kind
ellipticCKComplementary complete elliptic integral of the first kind
ellipticCPiComplementary complete elliptic integral of the third kind
ellipticEComplete and incomplete elliptic integrals of the second kind
ellipticFIncomplete elliptic integral of the first kind
ellipticKComplete elliptic integral of the first kind
ellipticNomeElliptic nome function
ellipticPiComplete and incomplete elliptic integrals of the third kind
ellipjJacobi elliptic functions
jacobiAMJacobi amplitude function
jacobiCDJacobi CD elliptic function
jacobiCNJacobi CN elliptic function
jacobiCSJacobi CS elliptic function
jacobiDCJacobi DC elliptic function
jacobiDNJacobi DN elliptic function
jacobiDSJacobi DS elliptic function
jacobiNCJacobi NC elliptic function
jacobiNDJacobi ND elliptic function
jacobiNSJacobi NS elliptic function
jacobiSCJacobi SC elliptic function
jacobiSDJacobi SD elliptic function
jacobiSNJacobi SN elliptic function
jacobiZetaJacobi zeta function

Dirac, Heaviside and Related Functions

diracDirac delta function
heavisideHeaviside step function
kroneckerDeltaKronecker delta function
rectangularPulseRectangular pulse function
triangularPulseTriangular pulse function

Airy and Bessel Functions

airyAiry function
besselh Bessel function of third kind (Hankel function) for symbolic expressions
besseliModified Bessel function of the first kind for symbolic expressions
besseljBessel function of the first kind for symbolic expressions
besselkModified Bessel function of the second kind for symbolic expressions
besselyBessel function of the second kind for symbolic expressions

Hypergeometric and Whittaker Functions

hypergeomHypergeometric function
kummerUConfluent hypergeometric Kummer U function
meijerGMeijer G-function
whittakerMWhittaker M function
whittakerWWhittaker W function

Lambert W and Wright Functions

lambertwLambert W function
wrightOmegaWright omega function