25 relations: Analytic continuation, Andrei Slavnov, Divergent series, Emilio Elizalde, Extended real number line, Francisco José Ynduráin, Geometric series, Grandi's series, Harmonic series (mathematics), Limit of a sequence, Mathematics, Monotonic function, P-adic number, Rational number, Real number, Residue (complex analysis), Riemann zeta function, Series (mathematics), Theoretical physics, Zeta function regularization, 1 + 2 + 3 + 4 + ⋯, 1 + 2 + 4 + 8 + ⋯, 1 − 1 + 2 − 6 + 24 − 120 + ..., 1 − 2 + 3 − 4 + ⋯, 1 − 2 + 4 − 8 + ⋯.
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
Andrei Alekseevich Slavnov (Андрей Алексеевич Славнов, born 22 December 1939, Moscow) is a Russian theoretical physicist, known for Slavnov-Taylor identities.
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.
Emilio Elizalde (born March 8, 1950) is a Spanish physicist working in the fields of gravitational physics and general relativity.
In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).
Francisco José Ynduráin Muñoz (23 December 1940 – 6 June 2008) was a Spanish theoretical physicist.
In mathematics, a geometric series is a series with a constant ratio between successive terms.
In mathematics, the infinite series 1 - 1 + 1 - 1 + \dotsb, also written \sum_^ (-1)^n is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.
In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
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.
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.
The infinite series whose terms are the natural numbers is a divergent series.
In mathematics, is the infinite series whose terms are the successive powers of two.
In mathematics, the divergent series was first considered by Euler, who applied summability methods to assign a finite value to the series.
In mathematics, 1 − 2 + 3 − 4 + ··· is the infinite series whose terms are the successive positive integers, given alternating signs.
In mathematics, is the infinite series whose terms are the successive powers of two with alternating signs.