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 function 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

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