Theorems · Theorem · complex analysis
Complex.sin_mul_sum_sin
∀ (n : ℕ) (a b : ℂ),
Complex.sin (a / 2) * ∑ i ∈ Finset.range n, Complex.sin (a * ↑i + b) =
Complex.sin (↑n * a / 2) * Complex.sin ((↑n - 1) * a / 2 + b)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- pow_oneproof · cited by 894
- Nat.cast_addproof · cited by 586
- Complex.cosproof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Finset.mul_sumproof · cited by 196
Cited by2
Results whose statement or proof uses this declaration.
- Complex.sum_sinproof · cited by 1
- Real.sin_mul_sum_sinproof · cited by 0