Search results
Results from the WOW.Com Content Network
An r-associated Stirling number of the second kind is the number of ways to partition a set of n objects into k subsets, with each subset containing at least r elements. [17] It is denoted by (,) and obeys the recurrence relation
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
Then the recurrence relation is used to successively compute trial values for , down to . Noting that a second sequence obtained from the trial sequence by multiplication by a constant normalizing factor will still satisfy the same recurrence relation, one can then apply a separate normalizing relationship to determine the normalizing factor ...
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
Stirling numbers express coefficients in expansions of falling and rising factorials (also known as the Pochhammer symbol) as polynomials.. That is, the falling factorial, defined as = (+) , is a polynomial in x of degree n whose expansion is
Consider the second-order linear differential equation ″ + ′ + () = Suppose a 2 is nonzero for all z.Then we can divide throughout to obtain ″ + () ′ + () = Suppose further that a 1 /a 2 and a 0 /a 2 are analytic functions.
The Pell numbers are defined by the recurrence relation: = {=; =; + In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that.
Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.