Ad
related to: convergent series function calculator math examplessolvely.ai has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence defines a series S that is denoted. The n th partial sum Sn is the sum of the first n terms of the sequence; that is, A series is convergent (or converges) if and only if the sequence of its partial sums tends to a limit ...
Series are classified not only by whether they converge or diverge, but also by the properties of the terms a n (absolute or conditional convergence); type of convergence of the series (pointwise, uniform); the class of the term a n (whether it is a real number, arithmetic progression, trigonometric function); etc.
Weierstrass M-test. In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex ...
A power series is here defined to be an infinite series of the form where j = (j1, …, jn) is a vector of natural numbers, the coefficients a(j1, …, jn) are usually real or complex numbers, and the center c = (c1, …, cn) and argument x = (x1, …, xn) are usually real or complex vectors. The symbol is the product symbol, denoting ...
Radius of convergence. In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal ...
In the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the good convergence behaviour of monotonic sequences, i.e. sequences that are non- increasing, or non- decreasing. In its simplest form, it says that a non-decreasing bounded -above sequence of real numbers converges to ...
A sequence of functions () converges uniformly to when for arbitrary small there is an index such that the graph of is in the -tube around f whenever . The limit of a sequence of continuous functions does not have to be continuous: the sequence of functions () = (marked in green and blue) converges pointwise over the entire domain, but the limit function is discontinuous (marked in red).
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Ad
related to: convergent series function calculator math examplessolvely.ai has been visited by 10K+ users in the past month