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NAME
euler - Euler number
SYNOPSIS
euler(n)
TYPES
n integer, n <= 1000000 if even
return integer
DESCRIPTION
Returns the Euler number with index n, i.e. the coefficient E_n in
the expansion
sech(t) = Sigma E_n * t^n/n!
When euler(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 euler(k) with 0 <= k <= n will be executed quickly.
If euler(k) is called with negative k, zero is returned and the
memory used by the table iu freed.
Considerable runtime and memory are required for calculating
euler(n) for large even n.
EXAMPLE
; for (n = 0; n <= 6; n++) print euler(n),; print;
1 0 -1 0 5 0 -61
LIMITS
none
LINK LIBRARY
NUMBER *qeuler(long n)
SEE ALSO
bernoulli, bell, catalan, comb, fact, perm
## Copyright (C) 2000,2021 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.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2000/12/14 01:33:00
## File existed as early as: 2000
##
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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