entire function of exponential type

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• Entire function — 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… …   Wikipedia

• Exponential family — Not to be confused with the exponential distribution. Natural parameter links here. For the usage of this term in differential geometry, see differential geometry of curves. In probability and statistics, an exponential family is an important… …   Wikipedia

• Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… …   Wikipedia

• Generating function — This article is about generating functions in mathematics. For generating functions in classical mechanics, see Generating function (physics). For signalling molecule, see Epidermal growth factor. In mathematics, a generating function is a formal …   Wikipedia

• Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex …   Wikipedia

• E-function — In mathematics, E functions are a type of power series that satisfy particular systems of linear differential equations.DefinitionA function f ( x ) is called of type E , or an E function [Carl Ludwig Siegel, Transcendental Numbers , p.33,… …   Wikipedia

• Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

• Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… …   Wikipedia

• Carlson's theorem — In mathematics, in the area of complex analysis, Carlson s theorem is a uniqueness theorem about a summable expansion of an analytic function. It is typically invoked to defend the uniqueness of a Newton series expansion. Carlson s theorem has… …   Wikipedia

• Lidstone series — In mathematics, certain types of entire functions can be expressed as a certain polynomial expansion known as the Lidstone series.Let f ( z ) be an entire function of exponential type less than ( N + 1)π, as defined below. Then f ( z ) can be… …   Wikipedia

• Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia