# cv.complicated variables – Is there any non-normal household \$mathcal{F}\$ of meromorphic features on \$|z| Answer

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cv.complicated variables – Is there any non-normal household \$mathcal{F}\$ of meromorphic features on \$|z|

It is well-known that if a household of meromorphic features will not be regular (within the sense of Montel) on some province, then the corresponding household of derivatives might or might not breathe regular on that province.

For instance, $$mathcal{F}:={f_n= nz, ninmathbb{N}}$$ will not be regular on $$|z|<1.$$ However, the corresponding household of derivatives $$mathcal{F’}={n}$$ is regular on $$|z|<1.$$
Furthermore, the household $$mathcal{G}:={nz^2}$$ and its by-product $$mathcal{G’}={2nz}$$ will not be regular on $$|z|<1.$$

Observe that the household $$mathcal{G}$$ has a zero of organize $$2$$ at $$z=0$$ on $$|z|<1$$ and its corresponding household of derivatives will not be regular.

With the above statement in intellect, I’m inquisitive to know the next:

Does there live a household of meromorphic features whose every zero is of multiplicity $$2$$ and which isn’t regular on $$|z|<1.$$ But the corresponding household of derivatives is regular?

Any ameliorate shall breathe largely appreciated.

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