Release calc version 2.11.3t0

help/bernoulli

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+NAME
+    bernoulli - Bernoulli number
+
+SYNOPSIS
+    bernoulli(n)
+
+TYPES
+    n		integer, n < 2^31 if even
+
+    return	rational
+
+DESCRIPTION
+    Returns the Bernoulli number with index n, i.e. the coefficient B_n in
+    the expansion
+
+		t/(exp(t) - 1) = Sum B_n * t^n/n!
+
+    bernouuli(n) is zero both for n < 0 and for n odd and > 2.
+    When bernoulli(n) is computed for positive even n, the values for
+    n and smaller positive even indices are stored in a table so that
+    a later call to bernoulli(k) with 0 <= k < n will be executed quickly.
+
+    Considerable runtime and memory are required for calculating
+    bernoulli(n) for large even n.  For n = 1000, the numerator has
+    1779 digits, the denominator 9 digits.
+
+    The memory used to store calculated bernoulli numbers is freed by
+    freebernoulli().
+
+EXAMPLE
+    > config("mode", "frac"),;
+    > for (n = 0; n <= 6; n++) print bernoulli(n),; print;
+    1 -1/2 1/6 0 -1/30 0 1/42
+
+LIMITS
+    n < 2^31-1
+
+LINK LIBRARY
+    NUMBER *qbernoulli(long n)
+
+SEE ALSO
+    euler, freebernoulli, catalan, comb, fact, perm
+
+## Copyright (C) 2000  Ernest Bowen
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
+##
+## @(#) $Revision: 29.2 $
+## @(#) $Id: sin,v 29.2 2000/06/07 14:02:33 chongo Exp $
+## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/sin,v $
+##
+## Under source code control:	2000/07/13
+## File existed as early as:	2000
+##
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/