Entire
Entire may refer to: * Entire function, a function that is holomorphic on the whole complex plane * Entire (animal) Neutering, from the Latin ''neuter'' ('of neither sex'), is the removal of an animal's reproductive organ, either all of it or a considerably large part. The male-specific term is castration, while spaying is usually reserved for female animals. ..., an indication that an animal is not neutered * Entire (botany), a term in botany {{Disambiguation ...
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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 has a root at , then , taking the limit value at , 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. A transcendental entire function is an entire function that is not a polynomial. Properties Every entire function can be represented as a power series f(z) = \sum_^\infty a_n z^n that converges everywhere in the complex plane, hence ...
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