OurBigBook.comSite Source code

Asymptotic sequence

Functions

(ϕ_{n})

form an asymptotic sequence at

x_{0}

when

ϕ_{n + 1} = o (ϕ_{n})

. The notation

f \sim \sum_{n \geq 0} a_{n} ϕ_{n}

means that for every

N \geq 0

,

f - \sum_{n = 0}^{N} a_{n} ϕ_{n} = o (ϕ_{N}) .

Successive division of the remainder by

ϕ_{N}

uniquely recovers every coefficient.

Table of contents 107 3

 Ancestors (5)

 Incoming links (4)