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complex analysis in several variables

the study of functions that depend differentiably on several complex variables

en-US/ˈkɑmplɛks æˈnælɪsɪs ˈɪn ˈsɛvəɹəl ˈvɛɹiəbəlz/
en-GB/ˈkɒmplɛks əˈnæləsɪs ˈɪn ˈsɛvɹəl ˈvɛəɹɪəbəlz/

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mathematical theory