Category

Series (mathematics)

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geometric progression

sequence of numbers where each term is found by multiplying the previous one by a fixed, non-zero number

infinite sum of monomials

absolute convergence

a property of infinite series

divergent series

infinite series that is not convergent

convergent series

infinite series that produces a finite sum

alternating series

infinite series in which the signs of the general terms alternate between positive and negative

Madhava of Sangamagrama

Indian mathematician and astronomer (c.1340-c.1425)

Dirichlet series

mathematical series

function spaces generalizing finite-dimensional p norm spaces

telescoping series

series whose partial sums eventually only have a fixed number of terms after cancellation

uniform convergence

mode of convergence of a function sequence

formal power series

generalization of a polynomial, where the number of terms is allowed to be infinite, defined algebraically without consideration of convergence (so that e.g. evaluation is not always defined)

Leibniz formula for π

alternating series which converges to π/4

Cauchy–Hadamard theorem

harmonic progression

progression formed by taking the reciprocals of an arithmetic progression

binomial series

Eisenstein series

series representing modular forms

asymptotic analysis

field of mathematics studying the limiting behavior of functions and sequences

hypergeometric function

special function defined by a hypergeometric series

Borel summation

summation method for divergent series

Sylvester's sequence

integer sequence in which each member of the sequence is the product of the previous members, plus one

Euler summation

summation method for some divergent series

asymptotic expansion

series which gives an approximation to a function as the argument tends to some point

conditional convergence

a property of infinite series

Riemann series theorem

Mertens' theorems

series of three theorems about the density of prime numbers

function series

series in which the summands are not just real or complex numbers but functions

series expansion

concept in mathematics

Mercator series

expansion of the logarithm

divergence of the sum of the reciprocals of the primes

Wikimedia list article

mathematical term

mathematical series

harmonic series with all terms containing the digit '9' removed

unconditional convergence

Order-independent convergence of a sequence

arithmetico-geometric sequence

result of the term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression

Gregory's series

mathematical power series defining arctan

Goldbach–Euler theorem

theorem stating that sum of 1/(k−1), where k ranges over positive integers of the form mⁿ for m≥2 and n≥2, equals 1

maximum eccentricity for which a power series for Kepler's equation converges

generalized hypergeometric function

family of power series in mathematics

Kolmogorov's three-series theorem

concept in probability theory

power series with rational exponents

Kronecker's lemma

Levi-Civita field

system of numbers with non-finite quantities

Ostrowski–Hadamard gap theorem

result on the analytic continuation of lacunary power series

Abelian and tauberian theorems

used in the summation of divergent series

Lévy–Steinitz theorem

Liouville–Neumann series

Concept in the theory of integral equations

Lauricella hypergeometric series

well defined hypergeometric series discovered by Giuseppe Lauricella

sequence transformation

A mathematic operator acting on a given space of sequences

orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series

mathematical series