In complex analysis, Mittag-Leffler's theorem concerns the existence of meromorphic functions with prescribed poles. Conversely, it can be used to express any meromorphic function as a sum of partial fractions. It is sister to the Weierstrass factorization theorem, which asserts existence of holomorphic functions with prescribed zeros.
The theorem is named after the Swedish mathematician Gösta Mittag-Leffler who published versions of the theorem in 1876 and 1884.[1][2][3]
- ^ Mittag-Leffler (1876). "En metod att analytiskt framställa en funktion af rational karakter, hvilken blir oändlig alltid och endast uti vissa föreskrifna oändlighetspunkter, hvilkas konstanter äro på förhand angifna". Öfversigt af Kongliga Vetenskaps-Akademiens förhandlingar Stockholm. 33 (6): 3–16.
- ^ Mittag-Leffler (1884). "Sur la représentation analytique des fonctions monogènes uniformes dʼune variable indépendante". Acta Mathematica. 4: 1–79. doi:10.1007/BF02418410. S2CID 124051413.
- ^ Turner, Laura E. (2013-02-01). "The Mittag-Leffler Theorem: The origin, evolution, and reception of a mathematical result, 1876–1884". Historia Mathematica. 40 (1): 36–83. doi:10.1016/j.hm.2012.10.002. ISSN 0315-0860.