The theory of functions of several complex variables is the branch of mathematics dealing with 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 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 locally square-integrable solutions to the n-dimensional Cauchy–Riemann equations.
Read more about Several Complex Variables: Historical Perspective
Famous quotes containing the words complex and/or variables:
“By “object” is meant some element in the complex whole that is defined in abstraction from the whole of which it is a distinction.”
—John Dewey (1859–1952)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)