Laguerre polynomial

Table of contents
- Generalized Laguerre polynomial Laguerre polynomial
  - Rodrigues formula Generalized Laguerre polynomial

Generalized Laguerre polynomial

The generalized Laguerre polynomial

L_{n}^{(α)}

is orthogonal on

[0, \infty)

for the weight

x^{α} e^{- x}

when

α > - 1

.

Rodrigues formula

A Rodrigues formula constructs an orthogonal polynomial by differentiating a weight multiplied by a power. For generalized Laguerre polynomials,

L_{n}^{(α)} (x) = \frac{x ^{- α} e ^{x}}{n !} \frac{d ^{n}}{d x ^{n}} (e^{- x} x^{n + α}) .

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Laguerre differential operator on polynomials
Past exam of the mathematics course of the University of Cambridge / 2009 / ib / Paper 1 / 14B / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 9F / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 14E / iv / Solution

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