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72 relations: Abel–Ruffini theorem, Alex Wilkie, Algebra, Algebraic differential equation, Algebraic function, Algebraic independence, Algebraic number, Algebraic number field, Algebraic operation, Alternating series, Analytic function, Antiderivative, Archimedes, Base (exponentiation), Bessel function, Bijection, Complex number, Complex-valued function, Continuous function, Degree of a field extension, Differential algebra, Dimensional analysis, E (mathematical constant), Elliptic function, Entire function, Euler's formula, Exponential function, Factorial, Ferdinand von Lindemann, First-order logic, Function (mathematics), Gamma function, Generalized function, Generalized hypergeometric function, Grégoire de Saint-Vincent, Hipparchus, Hyperbola, Hyperbolic function, Hyperbolic sector, Hypertranscendental function, Introductio in analysin infinitorum, Inverse function, J-invariant, Jyā, koti-jyā and utkrama-jyā, Leonhard Euler, Linear interpolation, List of special functions and eponyms, List of types of functions, List of zeta functions, Logarithm, ..., Mathematical analysis, Multiplicative inverse, Natural logarithm, Nth root, Olaf Pedersen, Polynomial, Ptolemy, Quadrature (mathematics), Rational function, Schanuel's conjecture, Series (mathematics), Sine, Special functions, Square root, The Quadrature of the Parabola, Theodor Schneider, Transcendental number, Transcendental number theory, Trigonometric functions, Trigonometric tables, University Press of Southern Denmark, Upper half-plane. Expand index (22 more) »
Abel–Ruffini theorem
In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.
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Alex Wilkie
Alex James Wilkie FRS (born 1948 in Northampton) is a British mathematician known for his contributions to Model theory and logic.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Algebraic differential equation
In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra.
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Algebraic function
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation.
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Algebraic independence
In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set is algebraically independent over K if and only if α is transcendental over K. In general, all the elements of an algebraically independent set S over K are by necessity transcendental over K, and over all of the field extensions over K generated by the remaining elements of S.
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Algebraic number
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).
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Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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Algebraic operation
In mathematics, a basic algebraic operation is any one of the traditional operations of arithmetic, which are addition, subtraction, multiplication, division, raising to an integer power, and taking roots (fractional power).
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Alternating series
In mathematics, an alternating series is an infinite series of the form with an > 0 for all n.
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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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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Archimedes
Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
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Base (exponentiation)
In exponentiation, the base is the number b in an expression of the form bn.
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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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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex-valued function
In mathematics, a complex-valued function (not to be confused with complex variable function) is a function whose values are complex numbers.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Degree of a field extension
In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension.
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Differential algebra
In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule.
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Dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.
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E (mathematical constant)
The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.
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Elliptic function
In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions.
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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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Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann (April 12, 1852 – March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that pi (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficients.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Generalized function
In mathematics, generalized functions, or distributions, are objects extending the notion of 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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Grégoire de Saint-Vincent
Grégoire de Saint-Vincent (22 March 1584 Bruges – 5 June 1667 Ghent) was a Flemish Jesuit and mathematician.
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Hipparchus
Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.
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Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
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Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
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Hyperbolic sector
A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy.
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Hypertranscendental function
A hypertranscendental function or transcendentally transcendental function is an analytic function which is not the solution of an algebraic differential equation with coefficients in Z (the integers) and with algebraic initial conditions.
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Introductio in analysin infinitorum
Introductio in analysin infinitorum (Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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J-invariant
In mathematics, Felix Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for defined on the upper half-plane of complex numbers.
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Jyā, koti-jyā and utkrama-jyā
Jyā, koti-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematicians and astronomers.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Linear interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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List of special functions and eponyms
This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym).
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List of types of functions
Functions can be identified according to the properties they have.
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List of zeta functions
In mathematics, a zeta function is (usually) a function analogous to the original example: the Riemann zeta function Zeta functions include.
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Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Nth root
In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.
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Olaf Pedersen
Olaf Pedersen (1920–1997) was a "leading authority on astronomy in classical antiquity and the Latin middle ages"Michael Hoskin (October 1998) Astronomy and Geophysics 39(5):33,4 Olaf Pedersen was born April 8, 1920 in Egtved, Jutland, Denmark.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Ptolemy
Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.
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Quadrature (mathematics)
In mathematics, quadrature is a historical term which means determining area.
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Rational function
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
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Schanuel's conjecture
In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions of the rational numbers.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Sine
In mathematics, the sine is a trigonometric function of an angle.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Square root
In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.
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The Quadrature of the Parabola
The Quadrature of the Parabola (Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC.
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Theodor Schneider
Theodor Schneider (7 May 1911, Frankfurt am Main – 31 October 1988, Freiburg im Breisgau) was a German mathematician, best known for providing proof of what is now known as the Gelfond–Schneider theorem.
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Transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.
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Transcendental number theory
Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with integer coefficients), in both qualitative and quantitative ways.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Trigonometric tables
In mathematics, tables of trigonometric functions are useful in a number of areas.
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University Press of Southern Denmark
University Press of Southern Denmark is Denmark's largest university press and was founded in 1966 as Odense University Press (Odense Universitetsforlag).
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Upper half-plane
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.
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Transcendent Function, Transcendent function, Transcendental functions, Trascendental function.
References
[1] https://en.wikipedia.org/wiki/Transcendental_function
