Theorems · Theorem · special functions
Complex.eventually_atTop_regularizedHGFunCoeff_ne_zero
∀ {a : Multiset ℂ} (b : Multiset ℂ),
(∀ j ∈ a, ∀ (k : ℕ), j ≠ -↑k) → ∀ᶠ (n : ℕ) in Filter.atTop, Complex.regularizedHGFunCoeff a b n ≠ 0If for all j and k : ℕ, a j ≠ -k, then the coefficients of the hypergeometric series
are eventually non-vanishing.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Filter.Eventuallystatement · cited by 3,134
- Multisetstatement and proof · cited by 2,627
- Filter.atTopstatement · cited by 2,405
- Complex.reproof · cited by 882
- Finset.supproof · cited by 530
- neg_subproof · cited by 272
- sub_neg_eq_addproof · cited by 264
- Multiset.toFinsetproof · cited by 230
- Nat.ceilproof · cited by 141
- Finset.le_supproof · cited by 112
- Filter.eventually_atTopproof · cited by 112
Cited by2
Results whose statement or proof uses this declaration.
- Complex.radius_regularizedHGFunSeries_eq_oneproof · cited by 1
- Complex.radius_regularizedHGFunSeries_eq_topproof · cited by 0