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

.

Table of contents
- Rodrigues formula Generalized Laguerre polynomial

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}) .

 Ancestors (9)

 Incoming links (3)

Laguerre projection kernel
Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 31 / 1 / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 17B / a / Solution

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