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)...

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...

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

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

poles. The gamma function has no zeros, so the reciprocal gamma function ⁠1/Γ(z)⁠ is an entire function. In fact, the gamma function corresponds to the...

everywhere and hence an entire function. The π-normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used...

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...

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...

In some sense, the Mittag-Leffler function is the simplest entire function of its order. The indicator function of E α ( z ) {\displaystyle E_{\alpha...

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...

is the sinc function, and also the zeroth spherical Bessel function. Since sinc is an even entire function (holomorphic over the entire complex plane)...

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...

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...

serves to define the eta function as an entire function. (The above relation and the facts that the eta function is entire and η ( 1 ) ≠ 0 {\displaystyle...

cosine functions to an imaginary angle. The hyperbolic sine and the hyperbolic cosine are entire functions. As a result, the other hyperbolic functions are...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...

number of operands a function takes Type, any proposition or set in the intuitionistic type theory Type, of an entire function Exponential type Type...

a function of a, b, or z with the other two held constant, this defines an entire function of a or z, except when b = 0, −1, −2, ... As a function of...

via the gamma function, and f 15 ( x ) {\displaystyle f_{15}(x)} is its reciprocal, an entire function. Finally, in the last function f 16 ( x ) {\displaystyle...

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

mathematics, and particularly complex dynamics, the escaping set of an entire function f {\displaystyle f} consists of all points that tend to infinity under...

Unsolved problem in mathematics Do all non-trivial zeroes of the Riemann zeta function have a real part of one half? More unsolved problems in mathematics In...

Functions in the complex plane can be extended to functions of complex quaternions (biquaternions). This includes not only entire functions whose power...

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...

bump function on the complex plane can be entire. In particular, on any connected open subset of the complex plane, there can be no bump function defined...

In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential...

In mathematics, the Riesz function is an entire function defined by Marcel Riesz in connection with the Riemann hypothesis, by means of the power series...

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...