archimedes.measure.LaguerreMeasure

class archimedes.measure.LaguerreMeasure

Measure for the Laguerre polynomial family.

Weight \(w(x) = e^{-x}\) on \([0, \infty)\).

The associated orthogonal polynomials are the (physicists’) Laguerre polynomials \(L_n(x)\). Moments of the weight are given by the Gamma function: \(\int_0^\infty x^k e^{-x} \, dx = k! = \Gamma(k+1)\).

__init__()

Methods

__init__()
affine_params([rate, start])	Map the reference weight onto a rate/shifted exponential weight \(w(x) = e^{-\mathrm{rate}(x - \mathrm{start})}\) on \([\mathrm{start}, \infty)\).
mass(*args, **kwargs)	Total mass of the measure mapped by affine_params(*args, **kwargs).
weight(x)	Weight function \(w(x) = e^{-x}\), evaluated at x.

Attributes

reference_mass	\(\int_0^\infty e^{-t} \, dt = 1\).
support	Support \([0, \infty)\).
uniform_weight	True if the weight is constant (weight(x) == weight(y)) for every x, y in support -- e.g. true for Legendre, false for Jacobi (singular at the endpoints) or Hermite/Laguerre (unbounded support).