Search results
Results from the WOW.Com Content Network
The series can be compared to an integral to establish convergence or divergence. Let f ( n ) = a n {\displaystyle f(n)=a_{n}} be a positive and monotonically decreasing function . If
Cauchy (1821) insisted on strict tests of convergence; he showed that if two series are convergent their product is not necessarily so, and with him begins the discovery of effective criteria. The terms convergence and divergence had been introduced long before by Gregory (1668).
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field of non-zero order k is written as =, a contraction of a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar.
Also convergence. The independent evolution of similar traits or adaptations in two or more different taxa from different periods or epochs in time, creating analogous structures that have similar form or function but were not present in the last common ancestor of those taxa; e.g. structures enabling flight evolved independently in at least ...
The two classical summation methods for series, ordinary convergence and absolute convergence, define the sum as a limit of certain partial sums. These are included only for completeness; strictly speaking they are not true summation methods for divergent series since, by definition, a series is divergent only if these methods do not work.
[28] [29] Other hearing genes also show convergence between echolocating taxa. [30] A genome-wide study of convergence published in 2013 analysed 22 mammal genomes and revealed that tens of genes have undergone the same replacements in echolocating bats and cetaceans, with many of these genes encoding proteins that function in hearing and ...
In a topological abelian group, convergence of a series is defined as convergence of the sequence of partial sums. An important concept when considering series is unconditional convergence, which guarantees that the limit of the series is invariant under permutations of the summands.