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64 lines
1.9 KiB
Plaintext
64 lines
1.9 KiB
Plaintext
NAME
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euler - Euler number
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SYNOPSIS
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euler(n)
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TYPES
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n integer, n <= 1000000 if even
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return integer
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DESCRIPTION
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Returns the Euler number with index n, i.e. the coefficient E_n in
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the expansion
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sech(t) = Sigma E_n * t^n/n!
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When euler(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 euler(k) with 0 <= k <= n will be executed quickly.
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If euler(k) is called with negative k, zero is returned and the
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memory used by the table iu freed.
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Considerable runtime and memery are required for calculating
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euler(n) for large even n.
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EXAMPLE
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; for (n = 0; n <= 6; n++) print euler(n),; print;
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1 0 -1 0 5 0 -61
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LIMITS
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none
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LINK LIBRARY
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NUMBER *qeuler(long n)
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SEE ALSO
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bernoulli, bell, 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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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## @(#) $Revision: 30.1 $
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## @(#) $Id: euler,v 30.1 2007/03/16 11:10:42 chongo Exp $
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## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/euler,v $
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##
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## Under source code control: 2000/12/14 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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