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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
74 lines
2.3 KiB
Plaintext
74 lines
2.3 KiB
Plaintext
NAME
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gd - gudermannian function
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SYNOPSIS
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gd(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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return number or "Log of zero or infinity" error value
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DESCRIPTION
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Calculate the gudermannian of z to a nultiple of eps with errors in
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real and imaginary parts less in absolute value than .75 * eps,
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or return an error value if z is close to one of the branch points
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at odd multiples of (pi/2) * i.
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gd(z) is usually defined initially for real z by one of the formulae
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gd(z) = 2 * atan(exp(z)) - pi/2
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= 2 * atan(tanh(z/2))
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= atan(sinh(z)),
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or as the integral from 0 to z of (1/cosh(t))dt. For complex z, the
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principal branch, approximated by gd(z, eps), has the cut:
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re(z) = 0, abs(im(z)) >= pi/2; on the cut calc takes gd(z) to be
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the limit as z is approached from the right or left according as
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im(z) > or < 0.
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If z = x + y*i and abs(y) < pi/2, gd(z) is given by
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gd(z) = atan(sinh(x)/cos(y)) + i * atanh(sin(y)/cosh(x)).
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EXAMPLE
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; print gd(1, 1e-5), gd(1, 1e-10), gd(1, 1e-15)
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.86577 .8657694832 .865769483239659
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; print gd(2+1i, 1e-5), gd(2+1i, 1e-10)
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1.42291+.22751i 1.4229114625+.2275106584i
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LIMITS
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none
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LINK LIBRARY
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COMPLEX *c_gd(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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agd, exp, ln, sin, sinh, etc.
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## Copyright (C) 1999 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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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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## 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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## distributed with calc under the filename COPYING-LGPL. You should have
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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 20:03:35
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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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