Theorems · Theorem · sequences and series
Stirling.log_stirlingSeq_sdiff_le
∀ (n : ℕ), Real.log (Stirling.stirlingSeq n) - Real.log (Stirling.stirlingSeq (n + 1)) ≤ 1 / (12 * ↑n * (↑n + 1))
Robbins' sharp stepwise bound for the Stirling sequence:
log (stirlingSeq n) - log (stirlingSeq (n+1)) ≤ 1 / (12 n (n + 1)).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- SummationFilter.unconditionalproof · cited by 2,068
- le_reflproof · cited by 2,061
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Real.logstatement and proof · cited by 939
- Real.expproof · cited by 871
Cited by3
Results whose statement or proof uses this declaration.
- Stirling.log_stirlingSeq_bounded_auxproof · cited by 1
- Stirling.log_stirlingSeq_sub_log_stirlingSeq_succproof · cited by 0
- Stirling.log_stirlingSeq_diff_leproof · cited by 0