Theorems · Theorem · special functions
ordinaryHypergeometricSeries_eq_zero_of_neg_nat
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : Field 𝕂] [inst_1 : Ring 𝔸] [inst_2 : Algebra 𝕂 𝔸] [inst_3 : TopologicalSpace 𝔸]
[inst_4 : IsTopologicalRing 𝔸] (a b c : 𝕂) {n k : ℕ},
↑k = -a ∨ ↑k = -b ∨ ↑k = -c → k < n → ordinaryHypergeometricSeries 𝔸 a b c n = 0If any parameter to the series is a sufficiently large nonpositive integer, then the series term is zero.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- Polynomial.evalproof · cited by 796
- Nat.factorialproof · cited by 616
- FormalMultilinearSeriesproof · cited by 615
- IsTopologicalRingstatement and proof · cited by 402
- zero_applyproof · cited by 251
Cited by3
Results whose statement or proof uses this declaration.
- ordinaryHypergeometric_radius_top_of_neg_nat₁proof · cited by 2
- ordinaryHypergeometric_radius_top_of_neg_nat₃proof · cited by 0
- ordinaryHypergeometricSeries_eq_zero_iffproof · cited by 0