suggestions for Gamma Functions section of docs

[James Theiler <jt@lanl.gov>]

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Hello,
  In a recent email, I made some suggestions for Section 7.9 [*] of 
the gsl-ref text.  I decided to go ahead and convert those general
remarks into some actual text, which I have attached.  What is 
attached specifically is a new version of specfunc-gamma.texi; since
i did a lot of re-arranging, the diff file is even longer than the
file itself.  I also made a few minor changes to the specfunc.texi 
file, and those changes are noted in the diff file below.
  As I mentioned, the most noticeable change is just to re-arrange
the functions in a way that I thought was more logical; with the
gamma functions first, followed by the incomplete gamma functions,
then the Pochhammer symbol (which is just a ratio of gamma functions),
then complete and incomplete beta functions, and then the various
factorials (fact, doublefact, lnfact, choose, etc) with the 
taylorcoeff as the last one in the list.  Less noticeable, I also 
changed some of the notation to be more consistent, and added a 
few notes of explanation to the Beta functions and Factorials 
subsections.
  By the way, in doing this, I was a little confused about how to
write texi files.  I think I finally figured out @c{...} and
@math{...} (they are quite confusing: if you do @math{expr} then you
get a math expression, but if you do @c{$expr$}@math{expr} then you
still get a single math expression; in the existing text, both
combinations appear, but it looks like @c{...} is used whenever the
latex is a little more complicated (eg, \ge vs >=)).  But I still
haven't figured out where the @example's appear.  On the web page, we
have in the Documentation section of the design document
(http://sources.redhat.com/gsl/design/gsl-design.html#SEC14) some good
comments regarding how to cite references, etc, but it would have been
useful to have some hints about what conventions the gsl reference
follows with respect to these texi commands.  Another by-the-way, the
"JT secton" of the Documentation page is essentially outdated by now.

regards,
jt

[*] I also made some comments for other sections of the documentation;
the changes in this email don't address those comments.

$ diff -C 2 gsl-1.6.91/doc/specfunc.texi gsl-1.6.91-new/doc/specfunc.texi
*** gsl-1.6.91/doc/specfunc.texi        2005-05-19 12:19:01.000000000 -0600
--- gsl-1.6.91-new/doc/specfunc.texi    2005-08-25 13:21:46.000000000 -0600
***************
*** 3,10 ****
  This chapter describes the GSL special function library.  The library
  includes routines for calculating the values of Airy functions, Bessel
! functions, Clausen functions, Coulomb wave functions, Coupling
  coefficients, the Dawson function, Debye functions, Dilogarithms,
  Elliptic integrals, Jacobi elliptic functions, Error functions,
! Exponential integrals, Fermi-Dirac functions, Gamma functions,
  Gegenbauer functions, Hypergeometric functions, Laguerre functions,
  Legendre functions and Spherical Harmonics, the Psi (Digamma) Function,
--- 3,10 ----
  This chapter describes the GSL special function library.  The 
library
  includes routines for calculating the values of Airy functions, Bessel
! functions, Beta functions, Clausen functions, Coulomb wave functions, Coupling
  coefficients, the Dawson function, Debye functions, Dilogarithms,
  Elliptic integrals, Jacobi elliptic functions, Error functions,
! Exponential integrals, Factorials, Fermi-Dirac functions, Gamma functions,
  Gegenbauer functions, Hypergeometric functions, Laguerre functions,
  Legendre functions and Spherical Harmonics, the Psi (Digamma) Function,
***************
*** 36,40 ****
  * Exponential Integrals::       
  * Fermi-Dirac Function::        
! * Gamma Function::              
  * Gegenbauer Functions::        
  * Hypergeometric Functions::    
--- 36,40 ----
  * Exponential Integrals::       
  * Fermi-Dirac Function::        
! * Gamma and Beta Functions::              
  * Gegenbauer Functions::        
  * Hypergeometric Functions::    
***************
*** 210,215 ****
  @include specfunc-fermi-dirac.texi
  
! @node Gamma Function
! @section Gamma Function
  @include specfunc-gamma.texi
  
--- 210,215 ----
  @include specfunc-fermi-dirac.texi
  
! @node Gamma and Beta Functions
! @section Gamma and Beta Functions
  @include specfunc-gamma.texi



-- 
James Theiler            Space and Remote Sensing Sciences
MS-B244, ISR-2, LANL     Los Alamos National Laboratory
Los Alamos, NM 87545     http://nis-www.lanl.gov/~jt





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