Theorems · Theorem · complex analysis
tendsto_logDeriv_euler_sin_div
∀ {x : ℂ},
x ∈ Complex.integerComplement →
Filter.Tendsto (fun n => logDeriv (fun z => ∏ j ∈ Finset.range n, (1 + sineTerm z j)) x) Filter.atTop
(nhds (logDeriv (fun t => Complex.sin (↑Real.pi * t) / (↑Real.pi * t)) x))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Finset.prodstatement · cited by 2,356
- Real.pistatement and proof · cited by 1,774
- Filter.univ_mem'proof · cited by 1,672
- Complex.ofRealstatement and proof · cited by 1,654
- Finset.rangestatement and proof · cited by 1,341
- Complex.sinstatement and proof · cited by 258
- logDerivstatement · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_logDeriv_euler_cot_subproof · cited by 1