Difference between revisions of "Hilger real part"

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=References=
 
=References=
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Hilger circle|next=Hilger imaginary part}}: Definition 2.3
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[[Category:Definition]]
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<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
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