ordinaryHypergeometricSeries_eq_zero_of_neg_nat

English

If a derivative Big-O condition holds for a punctured neighborhood around c, then g is not interval integrable on any interval through c.

Русский

Если выполняется условие Big-O для производной в пунктированной окрестности вокруг c, то g не интегрируем на любом интервале через c.

LaTeX

$$$\\neg \\text{IntervalIntegrable}(g, \\text{volume}, a, b)$ under punctured Big-O hypotheses$$

Lean4

/-- If any parameter to the series is a sufficiently large nonpositive integer, then the series
term is zero. -/
theorem ordinaryHypergeometricSeries_eq_zero_of_neg_nat {n k : ℕ} (habc : k = -a ∨ k = -b ∨ k = -c) (hk : k < n) :
    ordinaryHypergeometricSeries 𝔸 a b c n = 0 :=
  by
  rw [ordinaryHypergeometricSeries, ofScalars]
  rcases habc with h | h | h
  all_goals
    ext
    simp [(ascPochhammer_eval_eq_zero_iff n _).2 ⟨k, hk, h⟩]

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