[Maxima-commits] CVS: maxima/share/contrib/Zeilberger zeilberger.texi,1.2,1.3

[Robert D. <rob...@us...>]

Update of /cvsroot/maxima/maxima/share/contrib/Zeilberger
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv21531

Modified Files:
	zeilberger.texi 
Log Message:
Pasted in some examples for GosperSum.

Index: zeilberger.texi
===================================================================
RCS file: /cvsroot/maxima/maxima/share/contrib/Zeilberger/zeilberger.texi,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -d -r1.2 -r1.3
--- zeilberger.texi	10 Jan 2006 04:29:05 -0000	1.2
+++ zeilberger.texi	10 Jan 2006 05:00:54 -0000	1.3
@@ -103,6 +103,59 @@
 Returns the summmation of @var{F_k} from @math{@var{k} = @var{a}} to @math{@var{k} = @var{b}}
 if @var{F_k} has a hypergeometric anti-difference.
 Otherwise, @code{GosperSum} returns @code{nongosper_summable}.
+
+Examples:
+
+@c ===beg===
+@c load (zeilberger);
+@c GosperSum ((-1)^k*k / (4*k^2 - 1), k, 1, n);
+@c GosperSum (1 / (4*k^2 - 1), k, 1, n);
+@c GosperSum (x^k, k, 1, n);
+@c GosperSum ((-1)^k*a! / (k!*(a - k)!), k, 1, n);
+@c GosperSum (k*k!, k, 1, n);
+@c GosperSum ((k + 1)*k! / (k + 1)!, k, 1, n);
+@c GosperSum (1 / ((a - k)!*k!), k, 1, n);
+@c ===end===
+@example
+(%i1) load (zeilberger);
+(%o1)  /usr/share/maxima/share/contrib/Zeilberger/zeilberger.mac
+(%i2) GosperSum ((-1)^k*k / (4*k^2 - 1), k, 1, n);
+
+Dependent equations eliminated:  (1)
+                           3       n + 1
+                      (n + -) (- 1)
+                           2               1
+(%o2)               - ------------------ - -
+                                  2        4
+                      2 (4 (n + 1)  - 1)
+(%i3) GosperSum (1 / (4*k^2 - 1), k, 1, n);
+                                3
+                          - n - -
+                                2       1
+(%o3)                  -------------- + -
+                                2       2
+                       4 (n + 1)  - 1
+(%i4) GosperSum (x^k, k, 1, n);
+                          n + 1
+                         x          x
+(%o4)                    ------ - -----
+                         x - 1    x - 1
+(%i5) GosperSum ((-1)^k*a! / (k!*(a - k)!), k, 1, n);
+                                n + 1
+                a! (n + 1) (- 1)              a!
+(%o5)       - ------------------------- - ----------
+              a (- n + a - 1)! (n + 1)!   a (a - 1)!
+(%i6) GosperSum (k*k!, k, 1, n);
+
+Dependent equations eliminated:  (1)
+(%o6)                     (n + 1)! - 1
+(%i7) GosperSum ((k + 1)*k! / (k + 1)!, k, 1, n);
+                  (n + 1) (n + 2) (n + 1)!
+(%o7)             ------------------------ - 1
+                          (n + 2)!
+(%i8) GosperSum (1 / ((a - k)!*k!), k, 1, n);
+(%o8)                  nonGosper_summable
+@end example
 @end deffn
 
 @deffn {Function} parGosper (@var{F_@{n,k@}}, @var{k}, @var{n}, @var{d})