Theorems · Theorem · special functions
EulerSine.integral_cos_mul_cos_pow_aux
∀ {z : ℂ} {n : ℕ},
2 ≤ n →
z ≠ 0 →
∫ (x : ℝ) in 0..Real.pi / 2, Complex.cos (2 * z * ↑x) * ↑(Real.cos x) ^ n =
↑n / (2 * z) * ∫ (x : ℝ) in 0..Real.pi / 2, Complex.sin (2 * z * ↑x) * ↑(Real.sin x) * ↑(Real.cos x) ^ (n - 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites56
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
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- NormedAddCommGroupproof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- NontriviallyNormedFieldproof · cited by 8,742
- Complexstatement and proof · cited by 5,565
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement and proof · cited by 1,774
Cited by1
Results whose statement or proof uses this declaration.
- EulerSine.integral_cos_mul_cos_powproof · cited by 1