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
Trigonometric Functions
Hyperbolic Functions
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
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 |
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