: Mathematics: entire function

mathematical analysis > complex analysis > analytic function > holomorphic function > entire function

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entire function

In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function. If an entire function ${\\displaystyle f(z)}$ has a root at ${\\displaystyle w}$ , then ${\\displaystyle f(z)/(z-w)}$ , taking the limit value at ${\\displaystyle w}$ , is an entire function. On the other hand, the natural logarithm, the reciprocal function, and the square root are all not entire functions, nor can they be continued analytically to an entire function.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Entire_function)

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