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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:
L0 (x) = 1
L1 (x) = 1-x
(n+1)Ln+1 (x) = (2n+1-x)Ln (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 Ln (x) for any given x.
The LaguerreSum subroutine calculates the sum of Laguerre polynomials c0 L0 (x) + c1 L1 (x) + ... + cn Ln (x) using Clenshaw's recurrence formula.
The LaguerreCoefficients subroutine can represent Ln (x) as a sum of powers of x: c0 + c1 x + ... + cn x n.
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C#
C# 1.0 source.
laguerre.csharp.zip - Laguerre polynomials
C++
C++ source.
laguerre.cpp.zip - Laguerre polynomials
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)
Delphi
Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
laguerre.delphi.zip - Laguerre polynomials
Visual Basic 6
Visual Basic 6 source.
laguerre.vb6.zip - Laguerre polynomials
Zonnon beta
Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
laguerre.zonnon.zip - Laguerre polynomials
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