[Bug-gsl] specfunc-erf.texi

[Jorge Suit Perez Ronda]

Hi, this is not a bug in gsl but in the documentation (at least in my 
linux)

cd . \
 && makeinfo   \
      `echo gsl-ref.texi | sed 's,.*/,,'`
./specfunc-erf.texi:75: Misplaced {.
./specfunc-erf.texi:75: Misplaced }.
./specfunc-erf.texi:75: Misplaced {.
./specfunc-erf.texi:75: Misplaced }.
makeinfo: Removing output file 
`/home/jsperez/sourceforge/gsl/doc/gsl-ref.info' due to errors; use 
--force to preserve. make: *** [gsl-ref.info] Error 2

I have fixed line 75 changing  {} for ()

in any case here i attached the file.

best regards,

Jorge Suit

@cindex error function
@cindex erf(x)
@cindex erfc(x)

The error function is described in Abramowitz & Stegun, Chapter 7.  The
functions in this section are declared in the header file
@file{gsl_sf_erf.h}.

@menu
* Error Function::              
* Complementary Error Function::  
* Log Complementary Error Function::  
* Probability functions::       
@end menu

@node Error Function
@subsection Error Function

@deftypefun double gsl_sf_erf (double @var{x})
@deftypefunx int gsl_sf_erf_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the error function
@c{$\erf(x) = (2/\sqrt{\pi}) \int_0^x dt \exp(-t^2)$}
@math{erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2)}.

@comment Exceptional Return Values: none
@end deftypefun

@node Complementary Error Function
@subsection Complementary Error Function

@deftypefun double gsl_sf_erfc (double @var{x})
@deftypefunx int gsl_sf_erfc_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the complementary error function
@c{$\erfc(x) = 1 - \erf(x) = (2/\sqrt{\pi}) \int_x^\infty \exp(-t^2)$}
@math{erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2)}.

@comment Exceptional Return Values: none
@end deftypefun


@node Log Complementary Error Function
@subsection Log Complementary Error Function

@deftypefun double gsl_sf_log_erfc (double @var{x})
@deftypefunx int gsl_sf_log_erfc_e (double @var{x}, gsl_sf_result * 
@var{result})
These routines compute the logarithm of the complementary error function
@math{\log(\erfc(x))}.
@comment Exceptional Return Values: none
@end deftypefun


@node Probability functions
@subsection Probability functions

The probability functions for the Normal or Gaussian distribution are
described in Abramowitz & Stegun, Section 26.2.

@deftypefun double gsl_sf_erf_Z (double @var{x})
@deftypefunx int gsl_sf_erf_Z_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the Gaussian probability function @math{Z(x) =
(1/(2\pi)) \exp(-x^2/2)}.  
@end deftypefun

@deftypefun double gsl_sf_erf_Q (double @var{x})
@deftypefunx int gsl_sf_erf_Q_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the upper tail of the Gaussian probability
function @math{Q(x) = (1/(2\pi)) \int_x^\infty dt \exp(-t^2/2)}.
@comment Exceptional Return Values: none
@end deftypefun

@cindex hazard function

The "hazard function" for the normal distrbution,
also known as the inverse Mill's ratio, is defined as
@math{h(x) = Z(x)/Q(x) = \sqrt(2/\pi) \exp(-x^2 / 2) / \erfc(x/\sqrt(2))}.
It decreases rapidly as @math{x} approaches @math{-\infty} and asymptotes
to @math{h(x) \sim x} as @math{x} approaches @math{+\infty}.

@deftypefun double gsl_sf_hazard (double @var{x})
@deftypefunx int gsl_sf_hazard_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the hazard function for the normal distribution.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun