Theorems · Theorem · special functions
Complex.Gamma_one_half_eq
Complex.Gamma (1 / 2) = ↑Real.pi ^ (1 / 2)
The special-value formula Γ(1/2) = √π, which is equivalent to the Gaussian integral.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- LT.lt.leproof · cited by 2,189
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- one_divproof · cited by 624
- Real.sqrtproof · cited by 545
- Real.pi_posproof · cited by 173
- Complex.Gammastatement and proof · cited by 96
- Complex.ofReal_divproof · cited by 83
- Real.Gammaproof · cited by 76
- Complex.ofReal_invproof · cited by 62
Cited by3
Results whose statement or proof uses this declaration.
- Complex.Gammaℝ_oneproof · cited by 5
- Complex.hasDerivAt_Gammaℝ_oneproof · cited by 1
- Complex.digamma_one_halfproof · cited by 0