fpowerSeries_apply_one — Mathlib

English

The first coefficient of fpowerSeries of a constant fslope equals the corresponding term; specifically, fpowerSeries x 1 = (continuousMultilinearCurryFin1 𝕜 E F)^{-1} f.

Русский

Первый коэффициент fpowerSeries константной fslope равен соответствующему члены; конкретно, fpowerSeries x 1 = (continuousMultilinearCurryFin1 𝕜 E F)^{-1} f.

LaTeX

$$$ fpowerSeries\\_apply\\_one (f : E \\to L[𝕜] F) (x : E) : fpowerSeries x 1 = (continuousMultilinearCurryFin1 𝕜 E F).symm f $$$

Lean4

@[simp]
theorem fpowerSeries_apply_one (f : E →L[𝕜] F) (x : E) :
    f.fpowerSeries x 1 = (continuousMultilinearCurryFin1 𝕜 E F).symm f :=
  rfl

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