Theorems · Theorem · sequences and series
Real.summable_one_div_nat_add_rpow
∀ (a s : ℝ), (Summable fun n => 1 / |↑n + a| ^ s) ↔ 1 < s
- Defined in
- Mathlib.Analysis.PSeries
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites31
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
- Norm.normproof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Filter.EventuallyEqproof · cited by 1,912
- Nat.cast_zeroproof · cited by 1,870
- absstatement and proof · cited by 1,814
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Summablestatement and proof · cited by 778
- one_divproof · cited by 624
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