Theorems · Theorem · special functions
Complex.radius_regularizedHGFunSeries_eq_top_of_finite
∀ {a b : Multiset ℂ} {n : ℕ} {j : ℂ}, j ∈ a → j = -↑n → (Complex.regularizedHGFunSeries a b).radius = ⊤If there exists j and k : ℕ, such that a j = -k, then the hypergeometric series is finite
and has convergence radius ∞.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 289 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Complexstatement and proof · cited by 5,565
- Multisetstatement and proof · cited by 2,627
- FormalMultilinearSeries.radiusstatement · cited by 150
- Filter.eventually_atTopproof · cited by 112
- Complex.regularizedHGFunSeriesstatement and proof · cited by 8
- FormalMultilinearSeries.radius_eq_top_of_eventually_eq_zeroproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.radius_regularizedHGFunSeries_ge_oneproof · cited by 1
- Complex.radius_regularizedHGFunSeries_eq_topproof · cited by 0
- Complex.radius_regularizedGaussHGFunSeries_eq_top_of_leftproof · cited by 0
- Complex.radius_regularizedGaussHGFunSeries_eq_top_of_rightproof · cited by 0