Argument (z)

Aliases: Arg arg

argument (angle) of complex number.

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 (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 (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 (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 (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 (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 (n,t)

Dirichlet kernel of order n.

DiscreteDelta (v)

Returns 1 if and only if all elements are zero.

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 (n,t)

Fejer kernel of order n evaluated at t

See Planetmath for more information.

GammaFunction (x)

Aliases: Gamma

The Gamma function. Currently only implemented for real values.

See Planetmath or Wikipedia for more information.

KroneckerDelta (v)

Returns 1 if and only if all elements are equal.

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 (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 (func,x,incr)

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

MoebiusDiskMapping (a,z)

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

See Wikipedia or Planetmath for more information.

MoebiusMapping (z,z2,z3,z4)

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

See Wikipedia or Planetmath for more information.

MoebiusMappingInftyToInfty (z,z2,z3)

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

See Wikipedia or Planetmath for more information.

MoebiusMappingInftyToOne (z,z3,z4)

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

See Wikipedia or Planetmath for more information.

MoebiusMappingInftyToZero (z,z2,z4)

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

See Wikipedia or Planetmath for more information.

PoissonKernel (r,sigma)

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

PoissonKernelRadius (r,sigma)

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

RiemannZeta (x)

Aliases: zeta

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

See Planetmath or Wikipedia for more information.

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 (x)

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

deg2rad (x)

Convert degrees to radians.

rad2deg (x)

Convert radians to degrees.

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.