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In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane...

up entire in Wiktionary, the free dictionary. Entire may refer to: Entire function, a function that is holomorphic on the whole complex plane Entire (animal)...

the function has simple poles.[clarification needed] The gamma function has no zeros, so the reciprocal gamma function ⁠1/Γ(z)⁠ is an entire function. In...

analysis, the Weierstrass factorization theorem asserts that every entire function can be represented as a (possibly infinite) product involving its zeroes...

Cauchy in 1844), states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle f} for which there exists...

referred to as regular functions. A holomorphic function whose domain is the whole complex plane is called an entire function. The phrase "holomorphic...

arguments as functions C → C {\displaystyle \mathbb {C} \to \mathbb {C} } , are holomorphic over the entire complex plane, making them entire functions, while...

The exponential function is a mathematical function denoted by f ( x ) = exp ⁡ ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...

article. The Bessel function of the first kind is an entire function if α is an integer, otherwise it is a multivalued function with singularity at zero...

analytic everywhere and hence an entire function. The function has also been called the cardinal sine or sine cardinal function. The term sinc /ˈsɪŋk/ was introduced...

which is zero at the origin is an odd function and vice versa). Since the error function is an entire function which takes real numbers to real numbers...

so the Mittag-Leffler function is an entire function. This function is named after Gösta Mittag-Leffler. This class of functions are important in the theory...

properties that imply that an entire function is constant correspond to properties that ensure that a family of holomorphic functions is normal. For example...

imaginary part of any entire function will produce a harmonic function with the same singularity, so in this case the harmonic function is not determined...

of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the...

programming, an anonymous function (function literal, lambda abstraction, lambda function, lambda expression or block) is a function definition that is not...

mathematics, and particularly complex dynamics, the escaping set of an entire function ƒ consists of all points that tend to infinity under the repeated application...

analytic function. They are named after Émile Picard. Little Picard Theorem: If a function f : C → C {\textstyle f:\mathbb {C} \to \mathbb {C} } is entire and...

Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally...

the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order...