Imported Upstream version 1.72.0

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

diff --git a/libs/math/doc/sf/beta.qbk b/libs/math/doc/sf/beta.qbk
index f1c505b..e332fa5 100644 (file)
--- a/libs/math/doc/sf/beta.qbk
+++ b/libs/math/doc/sf/beta.qbk
@@ -26,14 +26,6 @@ The beta function is defined by:
 
 [optional_policy]
 
-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
 when T1 and T2 are different types.
 
@@ -78,13 +70,10 @@ This may not be the final solution, but it is very competitive compared to
 other implementation methods.
 
 The generic implementation - where no __lanczos approximation is available - is
-implemented in a very similar way to the generic version of the gamma function.
-Again in order to avoid numerical overflow the power terms that prefix the series and
-continued fraction parts are collected together into:
-
-[equation beta8]
-
-where la, lb and lc are the integration limits used for a, b, and a+b.
+implemented in a very similar way to the generic version of the gamma function
+by means of Sterling's approximation.
+Again in order to avoid numerical overflow the power terms that prefix the series
+are collected together
 
 There are a few special cases worth mentioning:
 
@@ -100,7 +89,7 @@ In addition:
 
 [equation beta7]
 
-[endsect][/section:beta_function The Beta Function]
+[endsect] [/section:beta_function The Beta Function]
 [/ 
   Copyright 2006 John Maddock and Paul A. Bristow.
   Distributed under the Boost Software License, Version 1.0.