.. _special-value-notations:

Special Value Notations
=======================


This topic defines notations of special values for complex functions.
The definitions are provided in text, tables, or formulas.


-  z, z1, z2, etc. denote complex numbers.

-  i, ``i2=-1`` is the imaginary unit.

-  x, X, x1, x2, etc. denote real imaginary parts.

-  y, Y, y1, y2, etc. denote imaginary parts.

-  X and Y represent any finite positive IEEE-754 floating point values, if not stated otherwise.

-  Quiet NaN and signaling NaN are denoted with QNAN and SNAN, respectively.

-  The IEEE-754 positive infinities or floating-point numbers are denoted with a ``+`` sign before X, Y, etc.

-  The IEEE-754 negative infinities or floating-point numbers are denoted with a ``-`` sign before X, Y, etc.


``CONJ(z)`` and ``CIS(z)`` are defined as follows:

- ``CONJ(x+i·y)=x-i·y``

- ``CIS(y)=cos(y)+i·sin(y)``.


The special value tables show the result of the function for the ``z``
argument at the intersection of the RE(z) column and the i\*IM(z) row. If
the function raises an exception on the argument ``z``, the lower part of
this cell shows the raised exception and the VM Error Status. An empty
cell indicates that this argument is normal and the result is defined
mathematically.