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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 polynomials and the exponential function, and any 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 f(z) has a root at w, then f(z)/(z−w) is an entire function. On the other hand, neither the natural logarithm nor the square root is an entire function, nor can they be continued analytically to an entire function.

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• Entire function
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• 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 polynomials and the exponential function, and any 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 f(z) has a root at w, then f(z)/(z−w) is an entire function. On the other hand, neither the natural logarithm nor the square root is an entire function, nor can they be continued analytically to an entire function.
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