Forward circle plus

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Let $h>0$ and $z_1,z_2 \in$ $\mathbb{C}_h$. Then we define the $\oplus_h$ operation by $$z_1 \oplus_h z_2 = z_1+z_2+z_1 z_2h.$$


Regressive functions form an abelian group under circle plus
Circle minus inverse of circle plus
Hilger real part oplus Hilger imaginary part equals z

See also

Forward circle minus