Search results
Results from the WOW.Com Content Network
A sequence can be thought of as a list of elements with a particular order. [1] [2] Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences.
(n factorial) is the number of n-permutations; !n (n subfactorial) is the number of derangements – n-permutations where all of the n elements change their initial places. In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original
Such a function is called a sequence, and, in this case the element is called the n th element of the sequence. The index notation can also be used for distinguishing some variables called parameters from the "true variables". In fact, parameters are specific variables that are considered as being fixed during the study of a problem.
An alternative method for deriving the same generating function uses the recurrence relation for the Bell numbers in terms of binomial coefficients to show that the exponential generating function satisfies the differential equation ′ = (). The function itself can be found by solving this equation. [11] [12] [13]
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple.
A parking function, in mathematics, is a finite sequence of positive integers with the property that, for every up to the sequence length, the sequence contains at least values that are at most . A sequence of this type, of length n {\displaystyle n} , describes the following process: a sequence of n {\displaystyle n} cars arrives on a street ...
A sequence is a function on the natural numbers, ... if and only if infinitely many elements of the sequence are in . ... Mathematics and its Applications 268 ...