Special functions | Analytic functions

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 f(z) has a root at w, then f(z) / (z − w), taking the limit value at 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. A transcendental entire function is an entire function that is not a polynomial. (Wikipedia).

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Integral domain | Unital algebra | Complex analysis | Fundamental theorem of algebra | Zero of a function | Fresnel integral | Associative algebra | Bessel function | Derivative | Prüfer domain | Liouville's theorem (complex analysis) | Fourier series | Up to | Carlson's theorem | Lacunary value | Radius of convergence | Riemann sphere | Polynomial | Weierstrass factorization theorem | Wiman-Valiron theory | Point at infinity | Transcendental function | Exponential function | Sequence | Casorati–Weierstrass theorem | Degree of a polynomial | Error function | Complex plane | Bounded function | Compact convergence | Mittag-Leffler function | Reciprocal gamma function | Function (mathematics) | Root of a function | Power series | Laguerre–Pólya class | Paley–Wiener theorem | Airy function | Holomorphic function | Cosine | Complex conjugate | Integral | Analytic continuation | Picard theorem | Barnes G-function | Exponential type | Natural logarithm | Square root | Jacques Hadamard | Fourier transform | Essential singularity | Jensen's formula | Parabolic cylinder function