Convolute

Description

Convolute[f, g, x] convolutes f(x) and g(x), i.e., \(TraditionalForm\`∫\_0\%1 dx\_1\ \(∫\_0\%1 dx\_2\ \(δ(x\  - \ x\_1\ x\_2)\)\ \(f(
                x\_1)\)\ \(\(g(x\_2)\)\(\ \)\(.\)\)\)\) Convolute[f, g] is equivalent to Convolute[f, g, x]. Convolute[exp, {x1, x2}] assumes that exp is polynomial in x1 and x2. Convolute uses table-look-up and does not do any integral calculations, only linear algebra.

Options[Convolute]

See also:  PlusDistribution.

Examples

Convolute[1, 1]

Convolute[x, x]

Convolute[1, x]

Convolute[1, (1/(1 - x))]

Convolute[1, PlusDistribution[(1/(1 - x))]]

Convolute[(1/(1 - x)), x]

Convolute[(1/(1 - x)), (1/(1 - x))]

Convolute[1, Log[1 - x]]

Convolute[1, x Log[1 - x]]

Convolute[(1/(1 - x)), Log[1 - x]]

Convolute[(1/(1 - x)), x Log[1 - x]]

Convolute[Log[1 - x]/(1 - x), x]

Convolute[1, x Log[x]]

Convolute[Log[1 - x], x]

Convolute[(1/(1 - x)), Log[x]/(1 - x)]

Convolute[1, Log[x]]

Convolute[x,  x Log[x]]

Convolute[(1/(1 - x)), Log[x]]

Convolute[1, Log[x]/(1 - x)]

Convolute[(1/(1 - x)), x Log[x]]

Convolute[Log[x]/(1 - x), x]

Convolute[1, x Log[x]]

Convolute[Log[x], x]

Convolute[(1/(1 - x)), Log[1 - x]/(1 - x)]