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1 handwiki Sirius Huang -- 1951 2022-10-26 01:40:42

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HandWiki. Several Complex Variables. Encyclopedia. Available online: https://encyclopedia.pub/entry/31538 (accessed on 24 September 2026).
HandWiki. Several Complex Variables. Encyclopedia. Available at: https://encyclopedia.pub/entry/31538. Accessed September 24, 2026.
HandWiki. "Several Complex Variables" Encyclopedia, https://encyclopedia.pub/entry/31538 (accessed September 24, 2026).
HandWiki. (2022, October 27). Several Complex Variables. In Encyclopedia. https://encyclopedia.pub/entry/31538
HandWiki. "Several Complex Variables." Encyclopedia. Web. 27 October, 2022.
Several Complex Variables
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The content is sourced from: https://handwiki.org/wiki/Several_complex_variables

The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions f(z1, z2, ... zn) on the space Cn of n-tuples of complex numbers. As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in the variables zi. Equivalently, as it turns out, they are locally uniform limits of polynomials; or local solutions to the n-dimensional Cauchy–Riemann equations.

complex variables local solutions n-tuples

References

  1. The field of complex numbers is a 2-dimensional vector space over real numbers.
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