Difference between revisions of "Signum"

From specialfunctionswiki
Jump to: navigation, search
(Videos)
 
(4 intermediate revisions by 2 users not shown)
Line 5: Line 5:
 
-1, & x < 0
 
-1, & x < 0
 
\end{array} \right.$$
 
\end{array} \right.$$
 +
The function is occasionally extended to a function $\mathrm{sgn} \colon \mathbb{C} \rightarrow \mathbb{C}$ by
 +
$$\mathrm{sgn}(z)=\dfrac{z}{|z|}.$$
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Signumplot.png|Graph of $\mathrm{sgn}$.
+
File:Signumplot.png|Graph of $\mathrm{sgn(x)}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
 +
 +
=Properties=
  
 
=Videos=
 
=Videos=
Line 17: Line 21:
  
 
=References=
 
=References=
 +
* {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|next=Signum}}: $(1.1.1)$
 +
* {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|prev=Signum|next=findme}}: $(1.1.2)$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 05:12, 11 February 2018

The signum function $\mathrm{sgn} \colon \mathbb{R} \rightarrow \{-1,0,1\}$ (also called the sign function) is the function $$\mathrm{sgn}(x)=\left\{ \begin{array}{ll} 1, & x > 0 \\ 0, & x = 0 \\ -1, & x < 0 \end{array} \right.$$ The function is occasionally extended to a function $\mathrm{sgn} \colon \mathbb{C} \rightarrow \mathbb{C}$ by $$\mathrm{sgn}(z)=\dfrac{z}{|z|}.$$

Properties

Videos

What is Signum Function in Mathematics - Learn Relations and Functions (28 January 2013)
Signum Function (26 August 2016)

References