# 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.

## Functions

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 `catalan` Catalan constant `eulergamma` Euler-Mascheroni constant

#### Logarithms

 `log` Natural logarithm of entries of symbolic matrix `log10` Log base 10 of symbolic input `log2` Base-2 logarithm of symbolic input

#### Polylogarithms and Zeta Function

 `dilog` Dilogarithm function `hurwitzZeta` Hurwitz zeta function `polylog` Polylogarithm `psi` Digamma function `zeta` Riemann zeta function

#### Trigonometric Functions

 `sin` Symbolic sine function `sinc` Normalized sinc function `cos` Symbolic cosine function `tan` Symbolic tangent function `cot` Symbolic cotangent function `sec` Symbolic secant function `csc` Symbolic cosecant function

#### Inverse Trigonometric Functions

 `asin` Symbolic inverse sine function `acos` Symbolic inverse cosine function `atan` Symbolic inverse tangent `acot` Symbolic inverse cotangent function `asec` Symbolic inverse secant function `acsc` Symbolic inverse cosecant function

#### Hyperbolic Functions

 `sinh` Symbolic hyperbolic sine function `cosh` Symbolic hyperbolic cosine function `tanh` Symbolic hyperbolic tangent function `coth` Symbolic hyperbolic cotangent function `sech` Symbolic hyperbolic secant function `csch` Symbolic hyperbolic cosecant function

#### Inverse Hyperbolic Functions

 `asinh` Symbolic inverse hyperbolic sine function `acosh` Symbolic inverse hyperbolic cosine function `atanh` Symbolic inverse hyperbolic tangent function `acoth` Symbolic inverse hyperbolic cotangent function `asech` Symbolic inverse hyperbolic secant function `acsch` Symbolic inverse hyperbolic cosecant function
 `abs` Symbolic absolute value (complex modulus or magnitude) `angle` Symbolic polar angle `atan2` Symbolic four-quadrant inverse tangent `conj` Complex conjugate of symbolic input `imag` Imaginary part of complex number `nthroot` Nth root of symbolic numbers `real` Real part of complex number `sign` Sign of real or complex value `signIm` Sign of the imaginary part of complex number

#### Gamma Functions

 `beta` Beta function `factorial` Factorial of symbolic input `gamma` Gamma function `gammaln` Logarithmic gamma function `igamma` Incomplete gamma function `nchoosek` Binomial coefficient `pochhammer` Pochhammer symbol

#### Error Functions

 `dawson` Dawson integral `erf` Error function `erfc` Complementary error function `erfcinv` Inverse complementary error function `erfi` Imaginary error function `erfinv` Inverse error function `fresnelc` Fresnel cosine integral function `fresnels` Fresnel sine integral function

#### Trigonometric Integrals

 `coshint` Hyperbolic cosine integral function `cosint` Cosine integral function `ei` One-argument exponential integral function `expint` Exponential integral function `eulergamma` Euler-Mascheroni constant `logint` Logarithmic integral function `sinhint` Hyperbolic sine integral function `sinint` Sine integral function `ssinint` Shifted sine integral function

#### Elliptic Integrals

 `ellipke` Complete elliptic integrals of the first and second kinds `ellipticCE` Complementary complete elliptic integral of the second kind `ellipticCK` Complementary complete elliptic integral of the first kind `ellipticCPi` Complementary complete elliptic integral of the third kind `ellipticE` Complete and incomplete elliptic integrals of the second kind `ellipticF` Incomplete elliptic integral of the first kind `ellipticK` Complete elliptic integral of the first kind `ellipticNome` Elliptic nome function `ellipticPi` Complete and incomplete elliptic integrals of the third kind
 `ellipj` Jacobi elliptic functions `jacobiAM` Jacobi amplitude function `jacobiCD` Jacobi CD elliptic function `jacobiCN` Jacobi CN elliptic function `jacobiCS` Jacobi CS elliptic function `jacobiDC` Jacobi DC elliptic function `jacobiDN` Jacobi DN elliptic function `jacobiDS` Jacobi DS elliptic function `jacobiNC` Jacobi NC elliptic function `jacobiND` Jacobi ND elliptic function `jacobiNS` Jacobi NS elliptic function `jacobiSC` Jacobi SC elliptic function `jacobiSD` Jacobi SD elliptic function `jacobiSN` Jacobi SN elliptic function `jacobiZeta` Jacobi zeta function

#### Dirac, Heaviside and Related Functions

 `dirac` Dirac delta function `heaviside` Heaviside step function `kroneckerDelta` Kronecker delta function `rectangularPulse` Rectangular pulse function `triangularPulse` Triangular pulse function

#### Airy and Bessel Functions

 `airy` Airy function `besselh` Bessel function of third kind (Hankel function) for symbolic expressions `besseli` Modified Bessel function of the first kind for symbolic expressions `besselj` Bessel function of the first kind for symbolic expressions `besselk` Modified Bessel function of the second kind for symbolic expressions `bessely` Bessel function of the second kind for symbolic expressions

#### Hypergeometric and Whittaker Functions

 `hypergeom` Hypergeometric function `kummerU` Confluent hypergeometric Kummer U function `meijerG` Meijer G-function `whittakerM` Whittaker M function `whittakerW` Whittaker W function

#### Lambert W and Wright Functions

 `lambertw` Lambert W function `wrightOmega` Wright omega function