Theorems · Theorem · complex analysis
tendsto_logDeriv_euler_cot_sub
∀ {x : ℂ},
x ∈ Complex.integerComplement →
Filter.Tendsto (fun n => ∑ j ∈ Finset.range n, cotTerm x j) Filter.atTop
(nhds (↑Real.pi * (↑Real.pi * x).cot - 1 / x))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Finset.sumstatement and proof · cited by 5,195
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Finset.rangestatement and proof · cited by 1,341
- Complex.sinproof · cited by 258
- logDerivproof · cited by 71
- Complex.integerComplementstatement and proof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- cot_series_rep'proof · cited by 2