CumulantGeneratingFunction (Built-in Mathematica Symbol)

CumulantGeneratingFunction[dist, t] gives the cumulant generating function for the symbolic distribution dist as a function of the variable t. ...

DeBruijnGraph (Built-in Mathematica Symbol)

DeBruijnGraph[m, n] gives the n-dimensional De Bruijn graph with m symbols.DeBruijnGraph[m, n, type] gives the De Bruijn graph with connectivity given by type.

LegendreP (Built-in Mathematica Symbol)

LegendreP[n, x] gives the Legendre polynomial P_n (x). LegendreP[n, m, x] gives the associated Legendre polynomial P_n^m(x).

Multinomial (Built-in Mathematica Symbol)

Multinomial[n_1, n_2, ...] gives the multinomial coefficient (n_1 + n_2 + ...)!/(n_1! n_2! ...).

ToeplitzMatrix (Built-in Mathematica Symbol)

ToeplitzMatrix[n] gives the n*n Toeplitz matrix with first row and first column being successive integers.ToeplitzMatrix[{c_1, c_2, ..., c_n}] gives the Toeplitz matrix whose ...

WalleniusHypergeometricDistribution (Built-in Mathematica Symbol)

WalleniusHypergeometricDistribution[n, n_succ, n_tot, w] represents a Wallenius noncentral hypergeometric distribution.

Verification of the Solution (Mathematica Tutorial)

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

Numerical Nonlinear Global Optimization ... (Mathematica Tutorial)

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...

LiftingWaveletTransform (Built-in Mathematica Symbol)

LiftingWaveletTransform[data] gives the lifting wavelet transform (LWT) of an array of data.LiftingWaveletTransform[data, wave] gives the lifting wavelet transform using the ...

CycleGraph (Built-in Mathematica Symbol)

CycleGraph[n] gives the cycle graph with n vertices C_n.