Theorems · Theorem · special functions
Real.Gamma_nat_add_one_add_half
∀ (k : ℕ), Real.Gamma (↑k + 1 + 1 / 2) = ↑(2 * k + 1).doubleFactorial * √Real.pi / 2 ^ (k + 1)
The special-value formula Γ(k + 1 + 1/2) = (2 * k + 1)‼ * √π / (2 ^ (k + 1)) for half-integer
values of the gamma function in terms of Nat.doubleFactorial.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
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- Real.pistatement and proof · cited by 1,774
- add_commproof · cited by 1,535
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- Nat.cast_addproof · cited by 586
- Real.sqrtstatement and proof · cited by 545
- zero_leproof · cited by 382
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpace.volume_ball_of_dim_oddproof · cited by 2
- Real.Gamma_nat_add_halfproof · cited by 0