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| | In [[complex analysis]], a mathematical discipline, the '''fundamental normality test''' gives sufficient conditions to test the normality of a [[Family (disambiguation)#Mathematics|family]] of [[analytic functions]]. |
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| | ==Statement of theorem== |
| | Let <math>\mathcal{F} </math> be a family of analytic functions defined on a domain <math> \Omega </math>. If there are two fixed complex numbers ''a'' and ''b'' that are omitted from the range of every ''ƒ'' ∈ <math>\mathcal{F}</math>, then <math> \mathcal{F} </math> is a [[normal family]] on <math> \Omega </math>. |
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| | The proof relies on properties of the [[elliptic modular function]] and can be found here: |
| | {{cite book | author = J. L. Schiff | title = Normal Families | publisher = Springer-Verlag | year = 1993 | isbn=0-387-97967-0 }} |
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| | ==See also== |
| | *[[Montel's theorem]] |
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| | [[Category:Complex analysis]] |
Latest revision as of 04:06, 9 January 2014
