/usr/share/calc/help/agd is in apcalc-common 2.12.5.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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agd - inverse gudermannian function
SYNOPSIS
agd(z [,eps])
TYPES
z number (real or complex)
eps nonzero real, defaults to epsilon()
return number or infinite error value
DESCRIPTION
Calculate the inverse gudermannian of z to a nultiple of eps with
errors in real and imaginary parts less in absolute value than .75 * eps,
or an error value if z is very close to one of the one of the branch
points of agd(z)..
agd(z) is usually defined initially for real z with abs(z) < pi/2 by
one of the formulae
agd(z) = ln(sec(z) + tan(z))
= 2 * atanh(tan(z/2))
= asinh(tan(z)),
or as the integral from 0 to z of (1/cos(t))dt. For complex z, the
principal branch, approximated by gd(z, eps), has cuts along the real
axis outside -pi/2 < z < pi/2.
If z = x + i * y and abs(x) < pi/2, agd(z) is given by
agd(z) = atanh(sin(x)/cosh(y)) + i * atan(sinh(y)/cos(x)>
EXAMPLE
; print agd(1, 1e-5), agd(1, 1e-10), agd(1, 1e-15)
1.22619 1.2261911709 1.226191170883517
; print agd(2, 1e-5), agd(2, 1e-10)
1.52345-3.14159i 1.5234524436-3.1415926536i
; print agd(5, 1e-5), agd(5, 1e-10), agd(5, 1e-15)
-1.93237 -1.9323667197 -1.932366719745925
; print agd(1+2i, 1e-5), agd(1+2i, 1e-10)
.22751+1.42291i .2275106584+1.4229114625i
LIMITS
none
LINK LIBRARY
COMPLEX *c_agd(COMPLEX *x, NUMBER *eps)
SEE ALSO
gd, exp, ln, sin, sinh, etc.
## 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: agd,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/agd,v $
##
## Under source code control: 1997/09/06 20:03:34
## File existed as early as: 1997
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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