Theorems · Theorem · real analysis
integral_sin_pow_odd
∀ (n : ℕ), ∫ (x : ℝ) in 0..Real.pi, Real.sin x ^ (2 * n + 1) = 2 * ∏ i ∈ Finset.range n, (2 * ↑i + 2) / (2 * ↑i + 3)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Finset.prodstatement and proof · cited by 2,356
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Finset.rangestatement and proof · cited by 1,341
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- le_of_ltproof · cited by 1,175
- sub_selfproof · cited by 996
Cited by2
Results whose statement or proof uses this declaration.
- integral_sin_pow_posproof · cited by 3
- Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_powproof · cited by 2