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,iis the imaginary unit.2=-1
- x,X,x1,x2, etc. denote real imaginary parts.
- y,Y,y1,y2, etc. denote imaginary parts.
- XandYrepresent any finite positive IEEE-754 floating point values, if not stated otherwise.
- QuietNaNand signalingNaNare denoted withQNANandSNAN, respectively.
- The IEEE-754 positive infinities or floating-point numbers are denoted with a+sign beforeX,Y, etc.
- The IEEE-754 negative infinities or floating-point numbers are denoted with a-sign beforeX,Y, etc.
CONJ(z)
and
CIS(z)
are defined as
follows:
CONJ(x+i
·
y)=x-i·
yCIS(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.