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?

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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?

jarakapak7 · Accepted Answer

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.

Consider the following function f ( x ) = ∑ k = 0 ∞ a...

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