powerSeriesFamily — Mathlib

English

If x has non-positive orderTop (not strictly positive), then powerSeriesFamily x f equals powerSeriesFamily 0 f for any power series f.

Русский

Если x имеет неположительную orderTop, то для любого powerSeries f выполняется равенство powerSeriesFamily x f = powerSeriesFamily 0 f.

LaTeX

$$powerSeriesFamily x f = powerSeriesFamily 0 f$$

Lean4

/-- A summable family given by scalar multiples of powers of a positive order Hahn series.

The scalar multiples are given by the coefficients of a power series. -/
abbrev powerSeriesFamily (x : HahnSeries Γ V) (f : PowerSeries R) : SummableFamily Γ V ℕ :=
  smulFamily (fun n => f.coeff n) (powers x)

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