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Post Closed as "too localized" by Deane Yang, Will Jagy, Qfwfq, André Henriques, J.C. Ottem
2 added 128 characters in body

lets assume we have a function $f : \mathbb{C}^{n} \rightarrow \mathbb{R}$ which is very nice (has all properties). Is then the complex hesse form of $f$ the same as the (real) hesse form of $f$ ? if they are not the same, then what is the connection between them ? is there any formula which brings them both in connection?

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# hessian and complex hessian

lets assume we have a function $f : \mathbb{C}^{n} \rightarrow \mathbb{R}$ which is very nice (has all properties). Is then the complex hesse form of $f$ the same as the (real) hesse form of $f$ ?