Difference between revisions of "Hilger real part"

From timescalewiki
Jump to: navigation, search
(Created page with "Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$")
 
 
(7 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
Let $h>0$ and let $z \in \mathbb{C}_h$, the [[Hilger complex plane]]. The Hilger real part of $z$ is defined by  
 
Let $h>0$ and let $z \in \mathbb{C}_h$, the [[Hilger complex plane]]. The Hilger real part of $z$ is defined by  
 
$$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$
 
$$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$
 +
 +
=Properties=
 +
[[Inequality for Hilger real part]]<br />
 +
[[Limit of Hilger real and imag parts yields classical]]<br />
 +
[[Hilger real part oplus Hilger imaginary part equals z]]<br />
 +
 +
=References=
 +
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Hilger circle|next=Hilger imaginary part}}: Definition 2.3
 +
 +
[[Category:Definition]]
 +
 +
<center>{{:Hilger complex plane footer}}</center>

Latest revision as of 15:41, 21 January 2023

Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$

Properties

Inequality for Hilger real part
Limit of Hilger real and imag parts yields classical
Hilger real part oplus Hilger imaginary part equals z

References

Hilger complex plane and friends

$\Huge\mathbb{A}_h$
Hilger alternating axis
$\Huge\mathbb{I}_h$
Hilger circle
$\Huge\mathbb{C}_h$
Hilger complex plane
$\Huge\mathrm{Im}_h$
Hilger imaginary part
$\Huge\mathring{\iota}$
Hilger pure imaginary
$\Huge\mathbb{R}_h$
Hilger real axis
$\Huge\mathrm{Re}_h$
Hilger real part