NAME
    asech - inverse hyperbolic secant

SYNOPSIS
    asech(x [,eps])

TYPES
    x		real, 0 < x <= 1
    eps		nonzero real, defaults to epsilon()

    return	real

DESCRIPTION
    Returns the asech of x to a multiple of eps with error less in
    absolute value than .75 * eps.

    asech(x) is the real number v for which sech(v) = x.  It is given by

		asech(x) = ln((1 + sqrt(1 - x^2))/x)

EXAMPLE
    ; print asech(.5,1e-5), asech(.5,1e-10), asech(.5,1e-15), asech(.5,1e-20)
    1.31696 1.3169578969 1.316957896924817 1.31695789692481670862

LIMITS
    none

LINK LIBRARY
    NUMBER *qasech(NUMBER *x, NUMBER *eps)

SEE ALSO
    asinh, acosh, atanh, acsch, acoth, epsilon

## Copyright (C) 1999  Landon Curt Noll
##
## 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.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: asech,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/asech,v $
##
## Under source code control:	1995/11/13 03:49:00
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
