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- Looman–Menchoff_theorem abstract "In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of the complex plane is holomorphic if and only if it satisfies the Cauchy–Riemann equations. It is thus a generalization of a theorem by Goursat, which instead of assuming the continuity of f, assumes its Fréchet differentiability when regarded as a function from a subset of R2 to R2.A complete statement of the theorem is as follows: Let Ω be an open set in C and f : Ω → C a continuous function. Suppose that the partial derivatives and exist everywhere but a countable set in Ω. Then f is holomorphic if and only if it satisfies the Cauchy–Riemann equation:".
- Looman–Menchoff_theorem wikiPageID "17523721".
- Looman–Menchoff_theorem wikiPageRevisionID "551432336".
- Looman–Menchoff_theorem subject Category:Theorems_in_complex_analysis.
- Looman–Menchoff_theorem comment "In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of the complex plane is holomorphic if and only if it satisfies the Cauchy–Riemann equations.".
- Looman–Menchoff_theorem label "Looman–Menchoff theorem".
- Looman–Menchoff_theorem label "Stelling van Looman-Menchoff".
- Looman–Menchoff_theorem sameAs Looman%E2%80%93Menchoff_theorem.
- Looman–Menchoff_theorem sameAs Stelling_van_Looman-Menchoff.
- Looman–Menchoff_theorem sameAs Q2309760.
- Looman–Menchoff_theorem sameAs Q2309760.
- Looman–Menchoff_theorem wasDerivedFrom Looman–Menchoff_theorem?oldid=551432336.