Theorems · Theorem · sequences and series
Stirling.log_stirlingSeq_sdiff_le_geo_sum
Deprecated since 2026-03-16Mathlib marks this declaration as deprecated.
∀ (n : ℕ),
Real.log (Stirling.stirlingSeq (n + 1)) - Real.log (Stirling.stirlingSeq (n + 2)) ≤
(1 / (2 * ↑(n + 1) + 1)) ^ 2 / (1 - (1 / (2 * ↑(n + 1) + 1)) ^ 2)We have a bound for successive elements in the sequence log (stirlingSeq k).
- Cited by
- 1 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.
Cites25
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
- SummationFilter.unconditionalproof · cited by 2,068
- le_of_ltproof · cited by 1,175
- Real.logstatement · cited by 939
- one_divproof · cited by 624
- HasSumproof · cited by 518
- zero_leproof · cited by 382
- mul_posproof · cited by 374
- two_ne_zeroproof · cited by 251
- Nat.cast_pos'proof · cited by 219
- pow_nonnegproof · cited by 141
- inv_powproof · cited by 140
Cited by1
Results whose statement or proof uses this declaration.
- Stirling.log_stirlingSeq_diff_le_geo_sumproof · cited by 0