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From "Brent Worden" <>
Subject RE: [math] matters of copyright
Date Mon, 02 Jun 2003 06:11:58 GMT
> specifically mentioned that is was based on "Numerical
> Recipes in C" which is not available under a license compatible with the
> ASL.

What is specifically mentioned was "is based on the formulas and
descriptions" found in NR and it clearly states in that "Of course, the mathematical
algorithms that underly the programs are not copyrightable..."

1) logGamma is derived using (6.1.3) and (6.1.5) from NR and the Paul
Godfrey's paper on Lanczos coefficients found at

2) regularizedGammaP is derived using (6.2.1) and (6.2.5) from NR.  I also
have hand-written notes on how I derived the implementation from those
formulas that I would be happy to provide for your viewing.

3) ChiSquaredDistribution and GammaDistribution are based on (6.2.1) and
(6.2.18) from NR and the fact that ChiSquared(v) ~ Gamma(v/2, 2) which can
be found in Casella and Berger.

The t-distribution patch has several modifications to the comments of all
the mentioned classes with links to all the cited material.

Also, the t patch makes use of other mathematical algorithms found in NR.

A) The continued fraction class is based on (5.2.1) and the modified Lentz
algorithm defined in that same section and accredited to Thompson and

B) logGamma uses the cf class and (6.2.7) from NR to provide better
convergence than the series.

C) logBeta uses (6.1.9) from NR.

D) regularizedBeta is derived using the cf class and (6.4.1), (6.4.5) and
(6.4.6) from NR.

E) TDistribution is based on (6.4.9) from NR.

Brent Worden

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