Theorems · Theorem · special functions
Real.deriv_Gamma_nat
∀ (n : ℕ), deriv Real.Gamma (↑n + 1) = ↑n.factorial * (-Real.eulerMascheroniConstant + ↑(harmonic n))
Explicit formula for the derivative of the Gamma function at positive integers, in terms of
harmonic numbers and the Euler-Mascheroni constant γ.
- Defined in
- Mathlib.NumberTheory.Harmonic.GammaDeriv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites73
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
- LE.le.transproof · cited by 3,151
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- le_antisymmproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- add_commproof · cited by 1,535
- Set.Ioiproof · cited by 1,463
Cited by2
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_Gamma_natproof · cited by 2
- Real.eulerMascheroniConstant_eq_neg_derivproof · cited by 1