Theorems · Theorem · special functions
Complex.Gamma_mul_Gamma_add_half
∀ (s : ℂ), Complex.Gamma s * Complex.Gamma (s + 1 / 2) = Complex.Gamma (2 * s) * 2 ^ (1 - 2 * s) * ↑√Real.pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites57
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
- Set.univproof · cited by 3,945
- Filter.Tendstoproof · cited by 3,814
- Compl.complproof · cited by 2,925
- nhdsWithinproof · cited by 1,912
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- div_eq_mul_invproof · cited by 715
- one_divproof · cited by 624
- zero_lt_oneproof · cited by 598
- Real.sqrtstatement and proof · cited by 545
Cited by2
Results whose statement or proof uses this declaration.
- Real.Gamma_mul_Gamma_add_halfproof · cited by 1
- Complex.Gammaℝ_mul_Gammaℝ_add_oneproof · cited by 1