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24
help/agd
24
help/agd
@@ -5,10 +5,10 @@ SYNOPSIS
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agd(z [,eps])
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TYPES
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z number (real or complex)
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eps nonzero real, defaults to epsilon()
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z number (real or complex)
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eps nonzero real, defaults to epsilon()
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return number or infinite error value
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return number or infinite error value
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DESCRIPTION
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Calculate the inverse Gudermannian of z to a multiple of eps with
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@@ -19,11 +19,11 @@ DESCRIPTION
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agd(z) is usually defined initially for real z with abs(z) < pi/2 by
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one of the formulae
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agd(z) = ln(sec(z) + tan(z))
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agd(z) = ln(sec(z) + tan(z))
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= 2 * atanh(tan(z/2))
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= 2 * atanh(tan(z/2))
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= asinh(tan(z)),
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= asinh(tan(z)),
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or as the integral from 0 to z of (1/cos(t))dt. For complex z, the
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principal branch, approximated by gd(z, eps), has cuts along the real
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@@ -31,7 +31,7 @@ DESCRIPTION
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If z = x + i * y and abs(x) < pi/2, agd(z) is given by
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agd(z) = atanh(sin(x)/cosh(y)) + i * atan(sinh(y)/cos(x)>
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agd(z) = atanh(sin(x)/cosh(y)) + i * atan(sinh(y)/cos(x)>
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EXAMPLE
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; print agd(1, 1e-5), agd(1, 1e-10), agd(1, 1e-15)
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@@ -63,7 +63,7 @@ SEE ALSO
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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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## 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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@@ -71,8 +71,8 @@ SEE ALSO
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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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## Under source code control: 1997/09/06 20:03:34
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## File existed as early as: 1997
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## Under source code control: 1997/09/06 20:03:34
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## File existed as early as: 1997
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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