describe gamma()`s behavior for negatives // mention that <complex> does not fulfill is.numeric()

git-svn-id: https://svn.r-project.org/R/trunk@87715 00db46b3-68df-0310-9c12-caf00c1e9a41

Author: maechler

doc/NEWS.Rd

@@ -196,6 +196,9 @@
       \item \code{optimize(f, *)} when \code{f(x)} is not finite says
       more about the value in its \code{warning} message.  It no longer
       replaces \code{-Inf} by the largest \emph{positive} finite number.
+
+      \item The documentation of \code{gamma} and \code{is.numeric} is more
+      specific, thanks to the contributors of \PR{18677}.
     }
   }
 

src/library/base/man/Special.Rd

@@ -1,6 +1,6 @@
 % File src/library/base/man/Special.Rd
 % Part of the R package, https://www.R-project.org
-% Copyright 1995-2022 R Core Team
+% Copyright 1995-2025 R Core Team
 % Distributed under GPL 2 or later
 
 \name{Special}
@@ -62,7 +62,15 @@ lfactorial(x)
   gamma function.  The gamma function is defined by
   (\bibcite{Abramowitz and Stegun section 6.1.1, page 255})
   \deqn{\Gamma(x) = \int_0^\infty t^{x-1} e^{-t} dt}{\Gamma(x) = integral_0^Inf t^(x-1) exp(-t) dt}
-  for all real \code{x} except zero and negative integers (when
+  for all \eqn{x > 0}, from which the recursions \eqn{\Gamma(x+1) =
+  x\Gamma(x)} and then \eqn{\Gamma(x+n) = (x+n-1)(x+n-2)\cdots x \Gamma(x)}
+  for all non-negative integers \eqn{n}.  Solving  for \eqn{\Gamma(x)} and
+  analytic continuation leads to the expression for non-integer negative real numbers,
+  \deqn{\Gamma(x) = \frac{\Gamma(x + n)}{(x + n -1) \cdots (x + 1)x}, \ n \in \mathbb{Z}^{+}, -n < x < 0,%
+  }{\Gamma(x) = \Gamma(x + n)/((x + n -1) ... (x + 1)x), n in N, -n < x < 0,}
+  see \bibcite{Abramowitz and Stegun (6.1.16 or 6.1.22, page 256)}.
+  %
+  The gamma function is not defined for zero and negative integers (when
   \code{NaN} is returned).  There will be a warning on possible loss of
   precision for values which are too close (within about
   \eqn{10^{-8}}{1e-8}) to a negative integer less than \samp{-10}.

src/library/base/man/numeric.Rd

@@ -39,7 +39,7 @@ is.numeric(x)
   function: you can write methods to handle specific classes of objects,
   see \link{InternalMethods}.  It is \strong{not} the same as
   \code{\link{is.double}}.  Factors are handled by the default method,
-  and there are methods for classes \code{"\link{Date}"},
+  and there are methods for classes \code{"\link{complex}"}, \code{"\link{Date}"},
   \code{"\link{POSIXt}"} and \code{"\link{difftime}"} (all of which
   return false).  Methods for \code{is.numeric} should only return true
   if the base type of the class is \code{double} or \code{integer}