Theorems · Theorem · complex analysis
Complex.sum_sin
∀ (n : ℕ) {a : ℂ},
(∀ (k : ℤ), a ≠ ↑k * (2 * ↑Real.pi)) →
∀ (b : ℂ),
∑ i ∈ Finset.range n, Complex.sin (a * ↑i + b) =
Complex.sin (↑n * a / 2) * Complex.sin ((↑n - 1) * a / 2 + b) / Complex.sin (a / 2)- Cited by
- 1 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- 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.sinstatement and proof · cited by 258
- Complex.sin_mul_sum_sinproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.sum_sinproof · cited by 0