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

Constants

`catalan`	Catalan constant
`eulergamma`	Euler–Mascheroni constant

Logarithms, Polylogarithms, and Zeta Function

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

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

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

Complex Numbers

`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 and Error Functions

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, Elliptic, and Other Integrals

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

Jacobi Elliptic Integrals & Zeta Function

`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

Other Special Functions

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