Theorems · Theorem · special functions
Complex.partialGamma_add_one
∀ {s : ℂ}, 0 < s.re → ∀ {X : ℝ}, 0 ≤ X → (s + 1).partialGamma X = s * s.partialGamma X - ↑(Real.exp (-X)) * ↑X ^ sThe recurrence relation for the indefinite version of the Γ function.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites52
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
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Continuousproof · cited by 2,592
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_reflproof · cited by 2,061
- Complex.ofRealstatement and proof · cited by 1,654
- add_commproof · cited by 1,535
Cited by1
Results whose statement or proof uses this declaration.
- Complex.GammaIntegral_add_oneproof · cited by 0