Difference between revisions of "Hilger real part"
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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 | ||
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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
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition 2.3
