Theorems · Definition · several complex variables
formalMultilinearSeries_geometric
(𝕜 : Type u_2) →
[inst : NontriviallyNormedField 𝕜] →
(A : Type u_7) → [inst_1 : NormedRing A] → [inst_2 : NormedAlgebra 𝕜 A] → FormalMultilinearSeries 𝕜 A AThe geometric series 1 + x + x ^ 2 + ... as a FormalMultilinearSeries.
- Defined in
- Mathlib.Analysis.Analytic.Constructions
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- FormalMultilinearSeriesstatement · cited by 615
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
Cited by12
Results whose statement or proof uses this declaration.
- formalMultilinearSeries_geometric_eq_ofScalarsstatement · cited by 3
- hasFPowerSeriesOnBall_inverse_one_substatement · cited by 3
- alternatingGeometricSeries_eq_formalMultilinearSeries_geometric_comp_negstatement · cited by 2
- one_le_formalMultilinearSeries_geometric_radiusstatement and proof · cited by 2
- hasFPowerSeriesOnBall_inverse_one_addproof · cited by 2
- hasFPowerSeriesOnBall_inv_one_substatement and proof · cited by 1
- analyticAt_inverse_one_subproof · cited by 1
- formalMultilinearSeries_geometric_apply_normstatement · cited by 0
- formalMultilinearSeries_geometric_apply_norm_lestatement · cited by 0
- formalMultilinearSeries_geometric_radiusstatement · cited by 0
- one_le_alternatingGeometricSeries_radiusproof · cited by 0
- analyticAt_inv_one_subproof · cited by 0