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Fowler's Dictionary of Modern English Usage, 4th edition, 2015 [40] "The so-called 'Oxford comma' is an optional comma that follows the penultimate item in a list of three or more items and precedes the word 'and' … The general rule is that it should be used consistently or not at all …
APA style (also known as APA format) is a writing style and format for academic documents such as scholarly journal articles and books. It is commonly used for citing sources within the field of behavioral and social sciences, including sociology, education, nursing, criminal justice, anthropology, and psychology.
The same definition can be used for series = whose terms are not numbers but rather elements of an arbitrary abelian topological group.In that case, instead of using the absolute value, the definition requires the group to have a norm, which is a positive real-valued function ‖ ‖: + on an abelian group (written additively, with identity element 0) such that:
The Cauchy product can be defined for series in the spaces (Euclidean spaces) where multiplication is the inner product. In this case, we have the result that if two series converge absolutely then their Cauchy product converges absolutely to the inner product of the limits.
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
With only two of six possible electrons in the shell, it is less than half-full and thus is the ground state. For sulfur (S) the lowest energy term is again 3 P {\displaystyle {}^{3}\!P\,} with spin–orbit levels J = 2 , 1 , 0 {\displaystyle J=2,1,0\,} , but now there are four of six possible electrons in the shell so the ground state is 3 P 2 ...
Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit. The alternating series test guarantees that an alternating series is convergent if the terms a n converge to 0 monotonically, but this condition is not necessary for convergence.