meromorphicTrailingCoeffAt_of_not_MeromorphicAt

English

If g is analytic at x and f equals (z-x)^n • g(z) in a punctured neighborhood (nhdsNE), then trailing coefficient equals g(x).

Русский

Если g аналитична в x и f совпадает с (z-x)^n • g(z) в окружности без x, то trailing coefficient совпадает с g(x).

LaTeX

$$$\\text{meromorphicTrailingCoeffAt}_f x = g x$ при $f =^?_{nhdsNe} (z-x)^n g(z)$ и $g$ аналитична.$$

Lean4

/-- If `f` is not meromorphic at `x`, the trailing coefficient is zero by definition.
-/
@[simp]
theorem meromorphicTrailingCoeffAt_of_not_MeromorphicAt (h : ¬MeromorphicAt f x) : meromorphicTrailingCoeffAt f x = 0 :=
  by simp [meromorphicTrailingCoeffAt, h]

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