Theorems · Theorem · special functions
EulerSine.integral_cos_pow_eq
∀ (n : ℕ), ∫ (x : ℝ) in 0..Real.pi / 2, Real.cos x ^ n = 1 / 2 * ∫ (x : ℝ) in 0..Real.pi, Real.sin x ^ n
Relate the integral cos x ^ n over [0, π/2] to the integral of sin x ^ n over [0, π],
which is studied in Mathlib/Analysis/Real/Pi/Wallis.lean and other places.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by2
Results whose statement or proof uses this declaration.
- EulerSine.integral_cos_pow_posproof · cited by 1
- EulerSine.sin_pi_mul_eqproof · cited by 1