Theorems · Theorem · special functions
Real.Gamma_one_half_eq
Real.Gamma (1 / 2) = √Real.pi
The special-value formula Γ(1/2) = √π, which is equivalent to the Gaussian integral.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- MeasureTheory.integralproof · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Set.Ioiproof · cited by 1,463
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- le_of_ltproof · cited by 1,175
Cited by6
Results whose statement or proof uses this declaration.
- Complex.Gamma_one_half_eqproof · cited by 3
- Real.Gamma_nat_add_one_add_halfproof · cited by 2
- EuclideanSpace.volume_ballproof · cited by 2
- Real.doublingGamma_oneproof · cited by 1
- Real.hasDerivAt_Gamma_one_halfproof · cited by 1
- Real.Gamma_nat_add_halfproof · cited by 0