Theorems · Theorem · complex analysis
meromorphicTrailingCoeffAt_of_not_MeromorphicAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜}, ¬MeromorphicAt f x → meromorphicTrailingCoeffAt f x = 0If f is not meromorphic at x, the trailing coefficient is zero by definition.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 200 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- MeromorphicAtstatement and proof · cited by 160
- meromorphicTrailingCoeffAtstatement · cited by 61
Cited by7
Results whose statement or proof uses this declaration.
- meromorphicTrailingCoeffAt_congr_nhdsNEproof · cited by 7
- ValueDistribution.circleIntegrable_log_meromorphicTrailingCoeffAtproof · cited by 2
- meromorphicTrailingCoeffAt_negproof · cited by 2
- MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_ltproof · cited by 2
- meromorphicTrailingCoeffAt_comp_add_const_eq_meromorphicTrailingCoeffAtproof · cited by 1
- meromorphicTrailingCoeffAt_invproof · cited by 1