Faster access than browser!
112 relations: Abramowitz and Stegun, Algebraic function, Analytic function, Archimedes, Aristotle, Asymptotic expansion, Bernoulli number, Big O notation, Binomial coefficient, Binomial series, Borel's lemma, Bounded function, Brook Taylor, Chebyshev polynomials, Clenshaw algorithm, Coefficient, Colin Maclaurin, Complex analysis, Complex number, Complex plane, Complex-valued function, Computer algebra system, Constant term, Continuous function, Convergence of random variables, Convergent series, Democritus, Derivative, Differential equation, Disk (mathematics), Divergent series, Dover Publications, E (mathematical constant), Einar Hille, Empty product, Entire function, Euler number, Euler's formula, Even and odd functions, Expected value, Exponential function, Exponentiation, Factorial, Finite difference, Fourier series, Fréchet space, Function (mathematics), Generating function, Geometric series, Gradient, ..., Harmonic analysis, Hessian matrix, Holomorphic function, Hyperbolic function, Indian mathematics, Integral, Integration by parts, Interval (mathematics), Inverse trigonometric functions, James Gregory (mathematician), Kerala School of Astronomy and Mathematics, Lars Hörmander, Laurent series, Law of large numbers, Limit of a sequence, Liu Hui, Logarithm, Logarithm of a matrix, Madhava of Sangamagrama, Madhava series, Mathematics, Matrix exponential, Meagre set, Meromorphic function, Method of exhaustion, Multi-index notation, Multiplicative inverse, Natural logarithm, Neighbourhood (mathematics), Newton polynomial, Non-analytic smooth function, Operator (mathematics), Padé approximant, Partial derivative, Periodic function, Pointwise convergence, Poisson distribution, Polynomial, Power series, Puiseux series, Radius of convergence, Random variable, Real analysis, Real number, Real-valued function, Residual (numerical analysis), Runge's phenomenon, Series (mathematics), Sine, Singularity (mathematics), Smoothness, Square root, Square-integrable function, Taylor series, Taylor's theorem, Transcendental function, Trigonometric functions, Uniform convergence, Weierstrass function, YouTube, Zeno of Elea, Zeno's paradoxes. Expand index (62 more) »
Abramowitz and Stegun
Abramowitz and Stegun (AS) is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST).
New!!: Taylor series and Abramowitz and Stegun · See more »
Algebraic function
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation.
New!!: Taylor series and Algebraic function · See more »
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
New!!: Taylor series and Analytic function · See more »
Archimedes
Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
New!!: Taylor series and Archimedes · See more »
Aristotle
Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.
New!!: Taylor series and Aristotle · See more »
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.
New!!: Taylor series and Asymptotic expansion · See more »
Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
New!!: Taylor series and Bernoulli number · See more »
Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
New!!: Taylor series and Big O notation · See more »
Binomial coefficient
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
New!!: Taylor series and Binomial coefficient · See more »
Binomial series
In mathematics, the binomial series is the Maclaurin series for the function f given by f(x).
New!!: Taylor series and Binomial series · See more »
Borel's lemma
In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations.
New!!: Taylor series and Borel's lemma · See more »
Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.
New!!: Taylor series and Bounded function · See more »
Brook Taylor
Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.
New!!: Taylor series and Brook Taylor · See more »
Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
New!!: Taylor series and Chebyshev polynomials · See more »
Clenshaw algorithm
In numerical analysis, the Clenshaw algorithm, Note that this paper is written in terms of the Shifted Chebyshev polynomials of the first kind T^*_n(x).
New!!: Taylor series and Clenshaw algorithm · See more »
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.
New!!: Taylor series and Coefficient · See more »
Colin Maclaurin
Colin Maclaurin (Cailean MacLabhruinn; 1 February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra.
New!!: Taylor series and Colin Maclaurin · See more »
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
New!!: Taylor series and Complex analysis · See more »
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.
New!!: Taylor series and Complex number · See more »
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
New!!: Taylor series and Complex plane · See more »
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.
New!!: Taylor series and Complex-valued function · See more »
Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
New!!: Taylor series and Computer algebra system · See more »
Constant term
In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.
New!!: Taylor series and Constant term · See more »
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.
New!!: Taylor series and Continuous function · See more »
Convergence of random variables
In probability theory, there exist several different notions of convergence of random variables.
New!!: Taylor series and Convergence of random variables · See more »
Convergent series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers.
New!!: Taylor series and Convergent series · See more »
Democritus
Democritus (Δημόκριτος, Dēmókritos, meaning "chosen of the people") was an Ancient Greek pre-Socratic philosopher primarily remembered today for his formulation of an atomic theory of the universe.
New!!: Taylor series and Democritus · See more »
Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
New!!: Taylor series and Derivative · See more »
Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
New!!: Taylor series and Differential equation · See more »
Disk (mathematics)
In geometry, a disk (also spelled disc).
New!!: Taylor series and Disk (mathematics) · See more »
Divergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
New!!: Taylor series and Divergent series · See more »
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
New!!: Taylor series and Dover Publications · See more »
E (mathematical constant)
The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.
New!!: Taylor series and E (mathematical constant) · See more »
Einar Hille
Carl Einar Hille (28 June 1894 – 12 February 1980) was an American mathematics professor and scholar.
New!!: Taylor series and Einar Hille · See more »
Empty product
In mathematics, an empty product, or nullary product, is the result of multiplying no factors.
New!!: Taylor series and Empty product · See more »
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.
New!!: Taylor series and Entire function · See more »
Euler number
In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.
New!!: Taylor series and Euler number · See more »
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.
New!!: Taylor series and Euler's formula · See more »
Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
New!!: Taylor series and Even and odd functions · See more »
Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
New!!: Taylor series and Expected value · See more »
Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
New!!: Taylor series and Exponential function · See more »
Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
New!!: Taylor series and Exponentiation · See more »
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.
New!!: Taylor series and Factorial · See more »
Finite difference
A finite difference is a mathematical expression of the form.
New!!: Taylor series and Finite difference · See more »
Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
New!!: Taylor series and Fourier series · See more »
Fréchet space
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.
New!!: Taylor series and Fréchet space · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Taylor series and Function (mathematics) · See more »
Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
New!!: Taylor series and Generating function · See more »
Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
New!!: Taylor series and Geometric series · See more »
Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
New!!: Taylor series and Gradient · See more »
Harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).
New!!: Taylor series and Harmonic analysis · See more »
Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
New!!: Taylor series and Hessian matrix · See more »
Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
New!!: Taylor series and Holomorphic function · See more »
Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
New!!: Taylor series and Hyperbolic function · See more »
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.
New!!: Taylor series and Indian mathematics · See more »
Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
New!!: Taylor series and Integral · See more »
Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
New!!: Taylor series and Integration by parts · See more »
Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
New!!: Taylor series and Interval (mathematics) · See more »
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
New!!: Taylor series and Inverse trigonometric functions · See more »
James Gregory (mathematician)
James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer.
New!!: Taylor series and James Gregory (mathematician) · See more »
Kerala School of Astronomy and Mathematics
The Kerala School of Astronomy and Mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
New!!: Taylor series and Kerala School of Astronomy and Mathematics · See more »
Lars Hörmander
Lars Valter Hörmander (24 January 1931 – 25 November 2012) was a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations".
New!!: Taylor series and Lars Hörmander · See more »
Laurent series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.
New!!: Taylor series and Laurent series · See more »
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.
New!!: Taylor series and Law of large numbers · See more »
Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
New!!: Taylor series and Limit of a sequence · See more »
Liu Hui
Liu Hui was a Chinese mathematician who lived in the state of Cao Wei during the Three Kingdoms period (220–280) of China.
New!!: Taylor series and Liu Hui · See more »
Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
New!!: Taylor series and Logarithm · See more »
Logarithm of a matrix
In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix.
New!!: Taylor series and Logarithm of a matrix · See more »
Madhava of Sangamagrama
Mādhava of Sangamagrāma, was a mathematician and astronomer from the town of Sangamagrama (believed to be present-day Aloor, Irinjalakuda in Thrissur District), Kerala, India.
New!!: Taylor series and Madhava of Sangamagrama · See more »
Madhava series
In mathematics, a Leibniz or Madhava series is any one of the series in a collection of infinite series expressions all of which are believed to have been discovered by Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics and later by Gottfried Wilhelm Leibniz, among others.
New!!: Taylor series and Madhava series · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Taylor series and Mathematics · See more »
Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
New!!: Taylor series and Matrix exponential · See more »
Meagre set
In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense small or negligible.
New!!: Taylor series and Meagre set · See more »
Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
New!!: Taylor series and Meromorphic function · See more »
Method of exhaustion
The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
New!!: Taylor series and Method of exhaustion · See more »
Multi-index notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
New!!: Taylor series and Multi-index notation · See more »
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.
New!!: Taylor series and Multiplicative inverse · See more »
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.
New!!: Taylor series and Natural logarithm · See more »
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
New!!: Taylor series and Neighbourhood (mathematics) · See more »
Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points.
New!!: Taylor series and Newton polynomial · See more »
Non-analytic smooth function
In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions.
New!!: Taylor series and Non-analytic smooth function · See more »
Operator (mathematics)
In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.
New!!: Taylor series and Operator (mathematics) · See more »
Padé approximant
In mathematics a Padé approximant is the 'best' approximation of a function by a rational function of given order – under this technique, the approximant's power series agrees with the power series of the function it is approximating.
New!!: Taylor series and Padé approximant · See more »
Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
New!!: Taylor series and Partial derivative · See more »
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
New!!: Taylor series and Periodic function · See more »
Pointwise convergence
In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.
New!!: Taylor series and Pointwise convergence · See more »
Poisson distribution
In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
New!!: Taylor series and Poisson distribution · See more »
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.
New!!: Taylor series and Polynomial · See more »
Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
New!!: Taylor series and Power series · See more »
Puiseux series
In mathematics, Puiseux series are a generalization of power series that allow for negative and fractional exponents of the indeterminate T. They were first introduced by Isaac Newton in 1676 and rediscovered by Victor Puiseux in 1850.
New!!: Taylor series and Puiseux series · See more »
Radius of convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.
New!!: Taylor series and Radius of convergence · See more »
Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
New!!: Taylor series and Random variable · See more »
Real analysis
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
New!!: Taylor series and Real analysis · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Taylor series and Real number · See more »
Real-valued function
In mathematics, a real-valued function is a function whose values are real numbers.
New!!: Taylor series and Real-valued function · See more »
Residual (numerical analysis)
Loosely speaking, a residual is the error in a result.
New!!: Taylor series and Residual (numerical analysis) · See more »
Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.
New!!: Taylor series and Runge's phenomenon · See more »
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.
New!!: Taylor series and Series (mathematics) · See more »
Sine
In mathematics, the sine is a trigonometric function of an angle.
New!!: Taylor series and Sine · See more »
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.
New!!: Taylor series and Singularity (mathematics) · See more »
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
New!!: Taylor series and Smoothness · See more »
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.
New!!: Taylor series and Square root · See more »
Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
New!!: Taylor series and Square-integrable function · See more »
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
New!!: Taylor series and Taylor series · See more »
Taylor's theorem
In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.
New!!: Taylor series and Taylor's theorem · See more »
Transcendental function
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
New!!: Taylor series and Transcendental function · See more »
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
New!!: Taylor series and Trigonometric functions · See more »
Uniform convergence
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
New!!: Taylor series and Uniform convergence · See more »
Weierstrass function
In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.
New!!: Taylor series and Weierstrass function · See more »
YouTube
YouTube is an American video-sharing website headquartered in San Bruno, California.
New!!: Taylor series and YouTube · See more »
Zeno of Elea
Zeno of Elea (Ζήνων ὁ Ἐλεάτης) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides.
New!!: Taylor series and Zeno of Elea · See more »
Zeno's paradoxes
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
New!!: Taylor series and Zeno's paradoxes · See more »
Redirects here:
Fractional Taylor series, Generalized taylor formula, List of Taylor series, MacLaurin series, Maclaurian series, Maclaurin polynomial, Maclaurin series, Maclaurin's series, Maclaurins series, Mclaurin series, Taylor Polymonial, Taylor Series, Taylor Series Expansion, Taylor coefficient, Taylor expansion, Taylor expansions, Taylor formula, Taylor polymonial, Taylor polynomial, Taylor polynomials, Taylor series expansion, Taylor's series, Taylor-Maclaurin series, Taylor-Mclaurin series.
References
[1] https://en.wikipedia.org/wiki/Taylor_series
