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ulises-jeremias committed Feb 22, 2018
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Expand Up @@ -55,3 +55,4 @@ cml/include/cml/config.h
build/*
tmp/*
install/*
docs/build/*
40 changes: 18 additions & 22 deletions docs/source/complex.rst
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Expand Up @@ -286,13 +286,13 @@ Complex Trigonometric Functions
Inverse Complex Trigonometric Functions
=======================================

.. function:: complex_t complex_arcsin (complex_t z)
.. function:: complex_t complex_asin (complex_t z)

This function returns the complex arcsine of the complex number :data:`z`,
:math:`\arcsin(z)`. The branch cuts are on the real axis, less than :math:`-1`
and greater than :math:`1`.

.. function:: complex_t complex_arcsin_real (real_t z)
.. function:: complex_t complex_asin_real (real_t z)

This function returns the complex arcsine of the real number :data:`z`,
:math:`\arcsin(z)`. For :math:`z` between :math:`-1` and :math:`1`, the
Expand All @@ -301,13 +301,13 @@ Inverse Complex Trigonometric Functions
and a positive imaginary part. For :math:`z` greater than :math:`1` the
result has a real part of :math:`\pi/2` and a negative imaginary part.

.. function:: complex_t complex_arccos (complex_t z)
.. function:: complex_t complex_acos (complex_t z)

This function returns the complex arccosine of the complex number :data:`z`,
:math:`\arccos(z)`. The branch cuts are on the real axis, less than :math:`-1`
and greater than :math:`1`.

.. function:: complex_t complex_arccos_real (real_t z)
.. function:: complex_t complex_acos_real (real_t z)

This function returns the complex arccosine of the real number :data:`z`,
:math:`\arccos(z)`. For :math:`z` between :math:`-1` and :math:`1`, the
Expand All @@ -316,33 +316,33 @@ Inverse Complex Trigonometric Functions
negative imaginary part. For :math:`z` greater than :math:`1` the result
is purely imaginary and positive.

.. function:: complex_t complex_arctan (complex_t z)
.. function:: complex_t complex_atan (complex_t z)

This function returns the complex arctangent of the complex number
:data:`z`, :math:`\arctan(z)`. The branch cuts are on the imaginary axis,
below :math:`-i` and above :math:`i`.

.. function:: complex_t complex_arcsec (complex_t z)
.. function:: complex_t complex_asec (complex_t z)

This function returns the complex arcsecant of the complex number :data:`z`,
:math:`\arcsec(z) = \arccos(1/z)`.

.. function:: complex_t complex_arcsec_real (real_t z)
.. function:: complex_t complex_asec_real (real_t z)

This function returns the complex arcsecant of the real number :data:`z`,
:math:`\arcsec(z) = \arccos(1/z)`.

.. function:: complex_t complex_arccsc (complex_t z)
.. function:: complex_t complex_acsc (complex_t z)

This function returns the complex arccosecant of the complex number :data:`z`,
:math:`\arccsc(z) = \arcsin(1/z)`.

.. function:: complex_t complex_arccsc_real (real_t z)
.. function:: complex_t complex_acsc_real (real_t z)

This function returns the complex arccosecant of the real number :data:`z`,
:math:`\arccsc(z) = \arcsin(1/z)`.

.. function:: complex_t complex_arccot (complex_t z)
.. function:: complex_t complex_acot (complex_t z)

This function returns the complex arccotangent of the complex number :data:`z`,
:math:`\arccot(z) = \arctan(1/z)`.
Expand Down Expand Up @@ -389,47 +389,47 @@ Complex Hyperbolic Functions
Inverse Complex Hyperbolic Functions
====================================

.. function:: complex_t complex_arcsinh (complex_t z)
.. function:: complex_t complex_asinh (complex_t z)

This function returns the complex hyperbolic arcsine of the
complex number :data:`z`, :math:`\arcsinh(z)`. The branch cuts are on the
imaginary axis, below :math:`-i` and above :math:`i`.

.. function:: complex_t complex_arccosh (complex_t z)
.. function:: complex_t complex_acosh (complex_t z)

This function returns the complex hyperbolic arccosine of the complex
number :data:`z`, :math:`\arccosh(z)`. The branch cut is on the real
axis, less than :math:`1`. Note that in this case we use the negative
square root in formula 4.6.21 of Abramowitz & Stegun giving
:math:`\arccosh(z)=\log(z-\sqrt{z^2-1})`.

.. function:: complex_t complex_arccosh_real (real_t z)
.. function:: complex_t complex_acosh_real (real_t z)

This function returns the complex hyperbolic arccosine of
the real number :data:`z`, :math:`\arccosh(z)`.

.. function:: complex_t complex_arctanh (complex_t z)
.. function:: complex_t complex_atanh (complex_t z)

This function returns the complex hyperbolic arctangent of the complex
number :data:`z`, :math:`\arctanh(z)`. The branch cuts are on the real
axis, less than :math:`-1` and greater than :math:`1`.

.. function:: complex_t complex_arctanh_real (real_t z)
.. function:: complex_t complex_atanh_real (real_t z)

This function returns the complex hyperbolic arctangent of the real
number :data:`z`, :math:`\arctanh(z)`.

.. function:: complex_t complex_arcsech (complex_t z)
.. function:: complex_t complex_asech (complex_t z)

This function returns the complex hyperbolic arcsecant of the complex
number :data:`z`, :math:`\arcsech(z) = \arccosh(1/z)`.

.. function:: complex_t complex_arccsch (complex_t z)
.. function:: complex_t complex_acsch (complex_t z)

This function returns the complex hyperbolic arccosecant of the complex
number :data:`z`, :math:`\arccsch(z) = \arcsinh(1/z)`.

.. function:: complex_t complex_arccoth (complex_t z)
.. function:: complex_t complex_acoth (complex_t z)

This function returns the complex hyperbolic arccotangent of the complex
number :data:`z`, :math:`\arccoth(z) = \arctanh(1/z)`.
Expand Down Expand Up @@ -465,7 +465,3 @@ following books,

* Dave Gillespie, Calc Manual, Free Software Foundation, ISBN
1-882114-18-3

.. rubric:: Footnotes

.. [#f1] Note that the first edition uses different definitions.
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