Theorems · Theorem · complex analysis
logDeriv_sin_div_eq_cot
∀ {x : ℂ},
x ∈ Complex.integerComplement →
logDeriv (fun t => Complex.sin (↑Real.pi * t) / (↑Real.pi * t)) x = ↑Real.pi * (↑Real.pi * x).cot - 1 / x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Nat.cast_oneproof · cited by 2,501
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- derivproof · cited by 676
- Complex.sinstatement and proof · cited by 258
- logDerivstatement and proof · cited by 71
- differentiableAt_idproof · cited by 63
- DifferentiableAt.compproof · cited by 38
- Complex.integerComplementstatement and proof · cited by 30
- Real.pi_ne_zeroproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_logDeriv_euler_cot_subproof · cited by 1