30 relations: Abel–Plana formula, Asymptotic expansion, Binomial transform, Cambridge University Press, Decimal representation, Dirichlet beta function, Dirichlet character, Dirichlet series, Euler number, Euler product, Euler–Maclaurin formula, Gottfried Wilhelm Leibniz, Gregory's series, Infinite product, Inverse trigonometric functions, Jonathan Borwein, List of formulae involving π, List of things named after Gottfried Leibniz, Madhava of Sangamagrama, Mathematics, Numerical integration, Pi, Prime number, Rate of convergence, Richardson extrapolation, Series acceleration, Shanks transformation, Squeeze theorem, Superparticular ratio, Van Wijngaarden transformation.
In mathematics, the Abel–Plana formula is a summation formula discovered independently by and.
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.
In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences.
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
A decimal representation of a non-negative real number r is an expression in the form of a series, traditionally written as a sum where a0 is a nonnegative integer, and a1, a2,...
In mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function.
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.
In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.
In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums.
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
Gregory's series, also known as the Madhava–Gregory series or Leibniz's series, is an infinite Taylor series expansion of the inverse tangent function.
In mathematics, for a sequence of complex numbers a1, a2, a3,...
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).
Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia.
The following is a list of significant formulae involving the mathematical constant pi.
Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher and mathematician.
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.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
The number is a mathematical constant.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence.
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series.
In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence.
In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, and sometimes the squeeze lemma, is a theorem regarding the limit of a function.
In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers.
In mathematics and numerical analysis, in order to accelerate convergence of an alternating series, Euler's transform can be computed as follows.
1 − 1 / 3 + 1 / 5 − 1 / 7 + ..., 1 − 1/3 + 1/5 − 1/7 + ..., Gregory's Series, Gregory-Leibniz series, Leibnitz series, Leibniz Series, Leibniz formula for pi, Leibniz series, Madhava-Leibniz, Madhava-Leibniz formula, Madhava-Leibniz formula for pi, Madhava-Leibniz series, Proof of Leibniz formula, Proof of leibniz formula.