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.