In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane. Typical examples of entire functions are the polynomials and the exponential function, and any sums, products and compositions of these, including the error function and the trigonometric functions sine and cosine and their hyperbolic counterparts the hyperbolic sine and hyperbolic cosine functions. Neither the natural logarithm nor the square root functions can be continued analytically to an entire function.
A transcendental entire function is an entire function that is not a polynomial (see transcendental function).
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