BellY[n, k, {x_1, ..., x n - k + 1}] gives the partial Bell polynomial Y n, k (x_1, ..., x n - k + 1). BellY[n, k, m] gives the generalized partial Bell polynomial of a ...

There are many Mathematica packages that implement symbolic mathematical operations. Here are a few examples drawn from the standard set of packages distributed with ...

Integrate[f, x] gives the indefinite integral \[Integral]f d x. Integrate[f, {x, x_min, x_max}] gives the definite integral \[Integral]_x_min^x_max\ f\ d x. Integrate[f, {x, ...

You can use the Mathematica function DSolve to find symbolic solutions to ordinary and partial differential equations. Solving a differential equation consists essentially in ...

Mathematica has fully integrated support for many of the tools used in classical and modern finance. These capabilities include financial instrument valuation, advanced time ...

LaplacianFilter[image, r] convolves image with a range r Laplacian kernel.LaplacianFilter[image, {r_1, r_2}] uses ranges r_i in the vertical and horizontal ...

LaplacianGaussianFilter[image, r] convolves image with a Laplacian-of-Gaussian kernel of pixel radius r.LaplacianGaussianFilter[image, {r, \[Sigma]}] convolves image with a ...

Important for elliptical shapes and periodic potentials, Mathematica achieves a new level of implementation for Mathieu-related functions, supporting arbitrary-precision ...

Some common operations on special functions. Most special functions have simpler forms when given certain specific arguments. Mathematica will automatically simplify special ...

MexicanHatWavelet[] represents the Mexican hat wavelet of width 1.MexicanHatWavelet[\[Sigma]] represents the Mexican hat wavelet of width \[Sigma].