Andreotti–Norguet Formula

(Theorems In Complex Analysis)

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Theorems In Complex Analysis since 1964
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What is Andreotti–Norguet formula?

The Andreotti–Norguet formula, first introduced by Aldo Andreotti and (is a higher–dimensional analogue of Cauchy integral formula for expressing the derivatives of a holomorphic function. Precisely, this formula express the value of the partial derivative of any multiindex order of a holomorphic function of several variables, in any interior point of a given bounded domain, as a hypersurface integral of the values of the function on the boundary of the domain itself. In this respect, it is analogous and generalizes the Bochner–Martinelli formula, reducing to it when the absolute value of the multiindex order of differentiation is 0. When considered for functions of n = 1 complex variables, it reduces to the ordinary Cauchy formula for the derivative of a holomorphic function: however, when n > 1, its integral kernel is not obtainable by simple differentiation of the Bochner–Martinelli kernel.

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several complex variabletheorems in complex analysisvariable

Synonyms

Andreotti-Norguet formulaAndreotti-Norguet fourmulaAndreotti-Norguet integral representationAndreotti–Norguet fourmulaAndreotti–Norguet integral representation

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