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68 lines
2.1 KiB
Plaintext
68 lines
2.1 KiB
Plaintext
NAME
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bernoulli - Bernoulli number
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SYNOPSIS
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bernoulli(n)
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TYPES
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n integer, n < 2^31 if even
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return rational
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DESCRIPTION
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Returns the Bernoulli number with index n, i.e. the coefficient B_n in
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the expansion
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t/(exp(t) - 1) = Sum B_n * t^n/n!
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bernoulli(n) is zero both for n < 0 and for n odd and > 2.
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When bernoulli(n) is computed for positive even n, the values for
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n and smaller positive even indices are stored in a table so that
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a later call to bernoulli(k) with 0 <= k < n will be executed quickly.
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Considerable runtime and memory are required for calculating
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bernoulli(n) for large even n. For n = 1000, the numerator has
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1779 digits, the denominator 9 digits.
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The memory used to store calculated bernoulli numbers is freed by
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freebernoulli().
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EXAMPLE
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> config("mode", "frac"),;
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> for (n = 0; n <= 6; n++) print bernoulli(n),; print;
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1 -1/2 1/6 0 -1/30 0 1/42
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LIMITS
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n < 2^31-1
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LIBRARY
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NUMBER *qbernoulli(long n)
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SEE ALSO
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euler, catalan, comb, fact, perm
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## Copyright (C) 2000 Ernest Bowen
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
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##
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## @(#) $Revision: 29.5 $
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## @(#) $Id: bernoulli,v 29.5 2002/07/10 11:47:04 chongo Exp $
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## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/bernoulli,v $
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##
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## Under source code control: 2000/07/13 01:33:00
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## File existed as early as: 2000
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##
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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