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Mathematical Functions

Mathematica has the most extensive collection of mathematical functions ever assembled. Often relying on original results and algorithms developed at Wolfram Research over the past two decades, each function supports a full range of symbolic operations, as well as efficient numerical evaluation to arbitrary precision, for all complex values of parameters.

ReferenceReference

Mathematical Constants »

Pi() ▪ E() ▪ Degree(°) ▪ EulerGamma ▪ ...

Complex Numbers »

I() ▪ Re ▪ Im ▪ Conjugate ▪ Abs ▪ Arg ▪ ...

Arithmetic Functions »

Plus(+) ▪ Times(×) ▪ Power(^) ▪ Sqrt ▪ Total ▪ ...

Numerical Functions »

Abs ▪ Round ▪ Floor ▪ Min ▪ Max ▪ Clip ▪ Rescale ▪ SquareWave ▪ ...

Elementary Functions »

Log ▪ Log10 ▪ Exp ▪ Sqrt ▪ Sin ▪ Cos ▪ Tan ▪ ArcTan ▪ Tanh ▪ Sinc ▪ ...

Special Functions »

Gamma ▪ Erf ▪ BesselJ ▪ BesselK ▪ AiryAi ▪ EllipticK ▪ LegendreP ▪ ChebyshevT ▪ HermiteH ▪ LaguerreL ▪ SpheroidalS1 ▪ JacobiSN ▪ WeierstrassP ▪ Zeta ▪ PolyLog ▪ EllipticTheta ▪ Hypergeometric2F1 ▪ HypergeometricPFQ ▪ MeijerG ▪ AppellF1 ▪ ...

Generalized Functions »

DiracDelta ▪ HeavisideTheta ▪ DiracComb ▪ ...

Integer Functions »

Mod ▪ Quotient ▪ Divisible ▪ GCD ▪ Factorial(!) ▪ Binomial ▪ Fibonacci ▪ BernoulliB ▪ StirlingS1 ▪ IntegerDigits ▪ DigitCount ▪ BitAnd ▪ ...

Number Theoretic Functions »

FactorInteger ▪ Prime ▪ PrimePi ▪ EulerPhi ▪ MoebiusMu ▪ DivisorSigma ▪ JacobiSymbol ▪ MultiplicativeOrder ▪ PartitionsP ▪ SquaresR ▪ DirichletL ▪ ...

Statistical Distributions »

NormalDistribution ▪ ChiSquareDistribution ▪ PoissonDistribution ▪ ...

Random Numbers »

RandomInteger ▪ RandomReal ▪ RandomChoice ▪ RandomPrime

Signals-Oriented Functions »

SquareWave ▪ TriangleWave ▪ UnitBox ▪ ...

N numerical evaluation to any precision

FunctionExpand expand in terms of simpler functions

FullSimplify apply full symbolic simplification