Theorems · Theorem · real analysis
Real.log_div_le_sum_range_add
∀ {x : ℝ},
0 ≤ x →
x < 1 →
∀ (n : ℕ),
1 / 2 * Real.log ((1 + x) / (1 - x)) ≤
∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1) + x ^ (2 * n + 1) / (1 - x ^ 2)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Finset.sumstatement and proof · cited by 5,195
- absproof · cited by 1,814
- Finset.rangestatement and proof · cited by 1,341
- Real.logstatement and proof · cited by 939
- abs_of_nonnegproof · cited by 279
- sub_le_iff_le_add'proof · cited by 41
- sub_nonneg_of_leproof · cited by 37
- Real.sum_range_le_log_divproof · cited by 1
- Real.sum_range_sub_log_div_leproof · cited by 1
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