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The graph of the square function y = x 2 is a parabola. The squaring operation defines a real function called the square function or the squaring function. Its domain is the whole real line, and its image is the set of nonnegative real numbers. The square function preserves the order of positive numbers: larger numbers have larger squares.
In analytic geometry, the graph of any quadratic function is a parabola in the xy-plane. Given a quadratic polynomial of the form a ( x − h ) 2 + k {\displaystyle a(x-h)^{2}+k} the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point ) of the parabola.
Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable.For this to be true, the integrals of the positive and negative portions of the real part must both be finite, as well as those for the imaginary part.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
Three iterations of the Peano curve construction, whose limit is a space-filling curve.. In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n-dimensional unit hypercube).
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Analytic continuation of natural logarithm (imaginary part) Analytic continuation is a technique to extend the domain of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.
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