Recurrent Sequence

a sequence a₀, a₁ a₂, … that satisfies a relationship in the form

a_{n + p} + C₁a_{n + p - 1} + … + C_pa_n = 0

where C₁, … ,C_p are constants. This relationship makes it possible to calculate, one after another, the members of the sequence if the first p members are known. The Fibonacci sequence 1, 1, 2, 3, 5, 8, … (a₀ = 1, a₁ = 1, …, a_{n + 2} = a_{n + i} + a_n) is a classical example of a recurrent sequence. The origin of the term “recurrent sequence” is associated with the name of A. de Moivre, who regarded power series a₀ + a₁x + a₂x² … with coefficients forming a recurrent sequence as being “recurrent series.” Such series always portray rational functions.

单词	recurrent sequence
释义	Recurrent Sequence Recurrent Sequence a sequence a₀, a₁ a₂, … that satisfies a relationship in the form a_{n + p} + C₁a_{n + p - 1} + … + C_pa_n = 0 where C₁, … ,C_p are constants. This relationship makes it possible to calculate, one after another, the members of the sequence if the first p members are known. The Fibonacci sequence 1, 1, 2, 3, 5, 8, … (a₀ = 1, a₁ = 1, …, a_{n + 2} = a_{n + i} + a_n) is a classical example of a recurrent sequence. The origin of the term “recurrent sequence” is associated with the name of A. de Moivre, who regarded power series a₀ + a₁x + a₂x² … with coefficients forming a recurrent sequence as being “recurrent series.” Such series always portray rational functions.
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