Theorems · Theorem · complex analysis
logDeriv_prod_sineTerm_eq_sum_cotTerm
∀ {x : ℂ},
x ∈ Complex.integerComplement →
∀ (n : ℕ), logDeriv (fun z => ∏ j ∈ Finset.range n, (1 + sineTerm z j)) x = ∑ j ∈ Finset.range n, cotTerm x j- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- logDerivstatement · cited by 71
- differentiableAt_idproof · cited by 63
- Complex.integerComplementstatement and proof · cited by 30
- cotTermstatement and proof · cited by 12
- sineTermstatement · cited by 10
- DifferentiableAt.div_constproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_logDeriv_euler_cot_subproof · cited by 1