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!

    bernoulli(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

LIBRARY
    NUMBER *qbernoulli(long n)

SEE ALSO
    euler, 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.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   2000/07/13 01:33:00
## File existed as early as:    2000
##
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
