Explore: Notions Of Recurrence

integer part of the continued fraction. The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas:

is included in most notions of sequence. It may be excluded depending on the context. A sequence can be thought of as a list of elements with a particular

eternal recurrence." By either interpretation the acceptance of eternal recurrence raises the question of whether it could justify a trans-valuation of one's

result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the

_{-n}}}=\infty .} The notions of ergodicity and null-recurrence are defined similarly by extending the corresponding notions of the standard birth-and-death

connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted

In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between

one work to those central to another, for example, the thought of the eternal recurrence features heavily in Also sprach Zarathustra (Thus Spoke Zarathustra)

the 17th century with notions of recursion, fractals have moved through increasingly rigorous mathematical treatment to the study of continuous but not differentiable

We prove the recurrence relation using the definition of Stirling numbers in terms of rising factorials. Distributing the last term of the product, we