Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / sf / lgamma.qbk

diff --git a/libs/math/doc/sf/lgamma.qbk b/libs/math/doc/sf/lgamma.qbk
index 428cb5d..5ea1a4e 100644 (file)
--- a/libs/math/doc/sf/lgamma.qbk
+++ b/libs/math/doc/sf/lgamma.qbk
@@ -35,14 +35,6 @@ which if non-null is set on output to the sign of tgamma(z).
 
 [graph lgamma]
 
-There are effectively two versions of this function internally: a fully
-generic version that is slow, but reasonably accurate, and a much more
-efficient approximation that is used where the number of digits in the significand
-of T correspond to a certain __lanczos.  In practice, any built-in
-floating-point type you will encounter has an appropriate __lanczos
-defined for it.  It is also possible, given enough machine time, to generate
-further __lanczos's using the program libs/math/tools/lanczos_generator.cpp.
-
 The return type of these functions is computed using the __arg_promotion_rules:
 the result is of type `double` if T is an integer type, or type T otherwise.
 
@@ -98,7 +90,7 @@ approximation.  The logarithmic version of the __lanczos is:
 
 [equation lgamm4]
 
-Where L[sub e,g][space] is the Lanczos sum, scaled by e[super g].
+Where L[sub e,g] is the Lanczos sum, scaled by e[super g].
 
 As before the reflection formula is used for /z < 0/.
 
@@ -116,8 +108,7 @@ form used is:
    lgamma(z) = (z-2)(z+1)(Y + R(z-2));
    
 Where Y is a constant, and R(z-2) is the rational approximation: optimised
-so that it's absolute error is tiny compared to Y.  In addition 
-small values of z greater
+so that its absolute error is tiny compared to Y.  In addition, small values of z greater
 than 3 can handled by argument reduction using the recurrence relation:
 
    lgamma(z+1) = log(z) + lgamma(z);
@@ -154,13 +145,13 @@ terms tend to zero, as /z -> 1/:
 
 [equation lgamm5]
 
-The C[sub k][space] terms in the above are the same as in the __lanczos.
+The C[sub k] terms in the above are the same as in the __lanczos.
 
 A similar rearrangement can be performed at /z = 2/:
 
 [equation lgamm6]
 
-[endsect][/section:lgamma The Log Gamma Function]
+[endsect] [/section:lgamma The Log Gamma Function]
 
 [/ 
   Copyright 2006 John Maddock and Paul A. Bristow.