= Mittag-Leffler's theorem
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= Mittag-Leffler theorem
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<Mittag-Leffler's theorem> prescribes the <principal parts> of a <meromorphic function>. Given an <open subset> $D$ of the complex plane, a subset $A$ having no accumulation point in $D$, and a finite sum of negative powers $P_a(z)=\sum_{j=1}^{m_a}c_{a,j}(z-a)^{-j}$ for each $a\in A$, there is a <meromorphic function> on $D$ with exactly these <principal parts> and no other <poles>. The difference of any two such <meromorphic functions> is a <holomorphic function> on $D$, because their <principal parts> cancel at every prescribed <pole>.
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