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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.
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.
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The concept of a homogeneous function was originally introduced for functions of several real variables.With the definition of vector spaces at the end of 19th century, the concept has been naturally extended to functions between vector spaces, since a tuple of variable values can be considered as a coordinate vector.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
For example, in lieu of a definition, Saunders Mac Lane in Mathematics, form and function summarizes the basics of several areas of mathematics, emphasizing their inter-connectedness, and observes: [175] the development of Mathematics provides a tightly connected network of formal rules, concepts, and systems.
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