- 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

. That is,`-1/e`

`LambertW`

is the inverse of the expression. Even for real`x*e^x`

`x`

this expression is not one to one and therefore has two branches over. See`[-1/e,0)`

`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

and less than 0. That is,`-1/e`

`LambertWm1`

is the second branch of the inverse of. See`x*e^x`

`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

. If you want the normalized function call`sin(x)/x`

.`sinc(pi*x)`

See Wikipedia for more information.

Version 1.0.16 onwards.