Functions

Argument
Argument (z)

Aliases: Arg arg

argument (angle) of complex number.

BesselJ0
BesselJ0 (x)

Bessel function of the first kind of order 0. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

BesselJ1
BesselJ1 (x)

Bessel function of the first kind of order 1. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

BesselJn
BesselJn (n,x)

Bessel function of the first kind of order n. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

BesselY0
BesselY0 (x)

Bessel function of the second kind of order 0. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

BesselY1
BesselY1 (x)

Bessel function of the second kind of order 1. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

BesselYn
BesselYn (n,x)

Bessel function of the second kind of order n. Only implemented for real numbers.

See Wikipedia for more information.

Version 1.0.16 onwards.

DirichletKernel
DirichletKernel (n,t)

Dirichlet kernel of order n.

DiscreteDelta
DiscreteDelta (v)

Returns 1 if and only if all elements are zero.

ErrorFunction
ErrorFunction (x)

Aliases: erf

The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt.

See Wikipedia or Planetmath for more information.

FejerKernel
FejerKernel (n,t)

Fejer kernel of order n evaluated at t

See Planetmath for more information.

GammaFunction
GammaFunction (x)

Aliases: Gamma

The Gamma function. Currently only implemented for real values.

See Planetmath or Wikipedia for more information.

KroneckerDelta
KroneckerDelta (v)

Returns 1 if and only if all elements are equal.

LambertW
LambertW (x)

The principal branch of Lambert W function computed for only real values greater than or equal to -1/e. That is, LambertW is the inverse of the expression x*e^x. Even for real x this expression is not one to one and therefore has two branches over [-1/e,0). See LambertWm1 for the other real branch.

See Wikipedia for more information.

Version 1.0.18 onwards.

LambertWm1
LambertWm1 (x)

The minus-one branch of Lambert W function computed for only real values greater than or equal to -1/e and less than 0. That is, LambertWm1 is the second branch of the inverse of x*e^x. See LambertW for the principal branch.

See Wikipedia for more information.

MinimizeFunction
MinimizeFunction (func,x,incr)

Find the first value where f(x)=0.

MoebiusDiskMapping
MoebiusDiskMapping (a,z)

Moebius mapping of the disk to itself mapping a to 0.

See Planetmath for more information.

MoebiusMapping
MoebiusMapping (z,z2,z3,z4)

Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity respectively.

See Planetmath for more information.

MoebiusMappingInftyToInfty
MoebiusMappingInftyToInfty (z,z2,z3)

Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 to 1 and 0 respectively.

See Planetmath for more information.

MoebiusMappingInftyToOne
MoebiusMappingInftyToOne (z,z3,z4)

Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 and infinity respectively.

See Planetmath for more information.

MoebiusMappingInftyToZero
MoebiusMappingInftyToZero (z,z2,z4)

Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 and infinity respectively.

See Planetmath for more information.

PoissonKernel
PoissonKernel (r,sigma)

Poisson kernel on D(0,1) (not normalized to 1, that is integral of this is 2pi).

PoissonKernelRadius
PoissonKernelRadius (r,sigma)

Poisson kernel on D(0,R) (not normalized to 1).

RiemannZeta
RiemannZeta (x)

Aliases: zeta

The Riemann zeta function. Currently only implemented for real values.

See Planetmath or Wikipedia for more information.

UnitStep
UnitStep (x)

The unit step function is 0 for x<0, 1 otherwise. This is the integral of the Dirac Delta function. Also called the Heaviside function.

See Wikipedia for more information.

cis
cis (x)

The cis function, that is the same as cos(x)+1i*sin(x)

deg2rad
deg2rad (x)

Convert degrees to radians.

rad2deg
rad2deg (x)

Convert radians to degrees.

sinc
sinc (x)

Calculates the unnormalized sinc function, that is sin(x)/x. If you want the normalized function call sinc(pi*x).

See Wikipedia for more information.

Version 1.0.16 onwards.