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45 relations: Airy function, Analytic function, Asymptote, Asymptotic expansion, Barnes integral, Bateman function, Bessel function, Bessel polynomials, Beta distribution, Binomial series, Branch point, Characteristic function (probability theory), Charlier polynomials, Confluence, Coulomb wave function, Crelle's Journal, Cunningham function, E. T. Whittaker, Elementary function, Entire function, Ernst Kummer, Error function, Exponential integral, Falling and rising factorials, Formal power series, Frobenius method, Gauss's continued fraction, Generalized hypergeometric function, Hermite polynomials, Hypergeometric function, Incomplete gamma function, Kelvin functions, Kummer's function, Laguerre polynomials, Laplace transform, Linear independence, Logarithmic integral function, Mathematics, Multiplication theorem, Parabolic cylinder function, Regular singular point, Singularity (mathematics), Toronto function, Trigonometric integral, Whittaker function.
Airy function
In the physical sciences, the Airy function (or Airy function of the first kind) Ai(x) is a special function named after the British astronomer George Biddell Airy (1801–92).
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
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Asymptotic expansion
In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.
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Barnes integral
In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions.
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Bateman function
In mathematics, the Bateman function (or k-function) is a special case of the confluent hypergeometric function studied by Harry Bateman(1931).
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Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Bessel polynomials
In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials.
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Beta distribution
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.
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Binomial series
In mathematics, the binomial series is the Maclaurin series for the function f given by f(x).
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Branch point
In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.
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Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.
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Charlier polynomials
In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier.
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Confluence
In geography, a confluence (also: conflux) occurs where two or more flowing bodies of water join together to form a single channel.
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Coulomb wave function
In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb.
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Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
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Cunningham function
In statistics, the Cunningham function or Pearson–Cunningham function ωm,n(x) is a generalisation of a special function introduced by and studied in the form here by.
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E. T. Whittaker
Edmund Taylor Whittaker FRS FRSE (24 October 1873 – 24 March 1956) was an English mathematician who contributed widely to applied mathematics, mathematical physics, and the theory of special functions.
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Elementary function
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
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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 at all finite points over the whole complex plane.
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Ernst Kummer
Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician.
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Error function
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
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Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane.
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Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.
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Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
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Frobenius method
In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form with in the vicinity of the regular singular point z.
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Gauss's continued fraction
In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions.
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Generalized hypergeometric function
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.
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Hermite polynomials
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.
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Hypergeometric function
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.
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Incomplete gamma function
In mathematics, the upper incomplete gamma function and lower incomplete gamma function are types of special functions, which arise as solutions to various mathematical problems such as certain integrals.
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Kelvin functions
In applied mathematics, the Kelvin functions berν(x) and beiν(x) are the real and imaginary parts, respectively, of where x is real, and, is the νth order Bessel function of the first kind.
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Kummer's function
In mathematics, there are several functions known as Kummer's function.
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Laguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are solutions of Laguerre's equation: which is a second-order linear differential equation.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Multiplication theorem
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function.
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Parabolic cylinder function
In mathematics, the parabolic cylinder functions are special functions defined as solutions to the differential equation This equation is found when the technique of separation of variables is used on Laplace's equation when expressed in parabolic cylindrical coordinates.
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Regular singular point
In mathematics, in the theory of ordinary differential equations in the complex plane \mathbb, the points of \mathbb are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity.
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Singularity (mathematics)
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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Toronto function
In mathematics, the Toronto function T(m,n,r) is a modification of the confluent hypergeometric function defined by, Weisstein, as.
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Trigonometric integral
In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions.
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Whittaker function
In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by to make the formulas involving the solutions more symmetric.
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1F1, Confluent hypergeometric equation, Confluent hypergeometric functions, Confluent hypergeometric series, Degenerated hypergeometric function, Kummer U function, Kummer series, Kummer's equation, Kummer's series, Tricomi Confluent hypergeometric function, Tricomi confluent hypergeometric function, Tricomi function, Tricomi hypergeometric function.
References
[1] https://en.wikipedia.org/wiki/Confluent_hypergeometric_function
