Consider the following function f ( x ) = <munderover> &#x2211;<!-- ∑ -->

abbracciopj

abbracciopj

Answered question

2022-06-20

Consider the following function
f ( x ) = k = 0 a k x k .
Let us say I know a k belongs to a strict subset F R .
I want to characterize the set of sequences { a k } k = 0 for which f ( x ) is a rational function in x.
Can someone point me to relevant results in literature?

Answer & Explanation

jarakapak7

jarakapak7

Beginner2022-06-21Added 14 answers

As
f ( x ) = p ( x ) q ( x ) ,
past a certain degree the coefficients of f ( x ) q ( x ) vanish.
Hence except for the first few, the a k are constrained by a linear recurrence on deg ( q ) + 1 terms.

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