Laguerre polynomials

Laguerre polynomials are defined as solutions of Laguerre's differential equation:

xy'' + (1-x)y' + ny = 0

Solutions corresponding to the non-negative integer n can be expressed using Rodrigues' formula

or can be constructed using the three term recurrence relation:

L(x) = 1
L(x) = 1-x
(n+1)Ln+1 (x) = (2n+1-x)L(x)-nLn-1 (x)

Unit description

The recurrence relation given above is the most efficient way to calculate the Laguerre polynomial. The LaguerreCalculate subroutine uses this relation to calculate L(x) for any given x.

The LaguerreSum subroutine calculates the sum of Laguerre polynomials cL(x) + cL(x) + ... + cL(x) using Clenshaw's recurrence formula.

The LaguerreCoefficients subroutine can represent L(x) as a sum of powers of x: c + cx + ... + cx n.

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