Theorems · Theorem · special functions
Real.BohrMollerup.tendsto_logGammaSeq
∀ {f : ℝ → ℝ} {x : ℝ},
ConvexOn ℝ (Set.Ioi 0) f →
(∀ {y : ℝ}, 0 < y → f (y + 1) = f y + Real.log y) →
0 < x → Filter.Tendsto (Real.BohrMollerup.logGammaSeq x) Filter.atTop (nhds (f x - f 1))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- TopologicalSpaceproof · cited by 24,529
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement and proof · cited by 2,405
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- Set.Ioistatement and proof · cited by 1,463
- Real.logstatement and proof · cited by 939
Cited by2
Results whose statement or proof uses this declaration.
- Real.eq_Gamma_of_log_convexproof · cited by 1
- Real.BohrMollerup.tendsto_log_gammaproof · cited by 1