GaussianMatrix (Built-in Mathematica Symbol)

GaussianMatrix[r] gives a matrix that corresponds to a Gaussian kernel of radius r. GaussianMatrix[{r, \[Sigma]}] gives a matrix corresponding to a Gaussian kernel with ...

FourierTransform (Built-in Mathematica Symbol)

FourierTransform[expr, t, \[Omega]] gives the symbolic Fourier transform of expr. FourierTransform[expr, {t_1, t_2, ...}, {\[Omega]_1, \[Omega]_2, ...}] gives the ...

InverseFourierTransform (Built-in Mathematica Symbol)

InverseFourierTransform[expr, \[Omega], t] gives the symbolic inverse Fourier transform of expr. InverseFourierTransform[expr, {\[Omega]_1, \[Omega]_2, \ ...}, {t_1, t_2, ...

KleinInvariantJ (Built-in Mathematica Symbol)

KleinInvariantJ[\[Tau]] gives the Klein invariant modular elliptic function J(\[Tau]).

LaplaceTransform (Built-in Mathematica Symbol)

LaplaceTransform[expr, t, s] gives the Laplace transform of expr. LaplaceTransform[expr, {t_1, t_2, ...}, {s_1, s_2, ...}] gives the multidimensional Laplace transform of ...

LogGamma (Built-in Mathematica Symbol)

LogGamma[z] gives the logarithm of the gamma function log \[CapitalGamma](z).

ArcTan (Built-in Mathematica Symbol)

ArcTan[z] gives the arc tangent tan -1 (z) of the complex number z. ArcTan[x, y] gives the arc tangent of y/x, taking into account which quadrant the point (x, y) is in.

LegendreQ (Built-in Mathematica Symbol)

LegendreQ[n, z] gives the Legendre function of the second kind Q_n (z). LegendreQ[n, m, z] gives the associated Legendre function of the second kind Q_n^m(z).

LogIntegral (Built-in Mathematica Symbol)

LogIntegral[z] is the logarithmic integral function li(z).

BesselI (Built-in Mathematica Symbol)

BesselI[n, z] gives the modified Bessel function of the first kind I_n (z).