Functii intregi si injective

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Cezar Lupu
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Functii intregi si injective

Post by Cezar Lupu »

Aratati ca toate functiile intregi si injective sunt de forma \( f(z)=az+b \) cu \( a, b\in\mathbb{C} \) si \( a\neq 0 \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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aleph
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Post by aleph »

f este polinom (cf. teoremei mari a lui Picard) iar pentru polinoame este simplu.
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Alin Galatan
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Post by Alin Galatan »

Varianta mai pentru incepatori e sa iei functia \( g(z)=f(\frac{1}{z}) \) si sa studiezi comportamentul in jurul lui 0.
Daca e singularitate esentiala, faci Cassorati, daca e pol, obtii concluzia, iar in ultimul caz ar inseamna ca f are limita la infinit, deci ar fi marginita, deci constanta.
(Hintul e dat in E. Stein, nu mi-a venit mie :))
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Cezar Lupu
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Post by Cezar Lupu »

Pai si eu tot de acolo o luasem. :)
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