Theorems · Theorem · sequences and series
Real.summable_abs_int_rpow
∀ {b : ℝ}, 1 < b → Summable fun n => |↑n| ^ (-b)- Defined in
- Mathlib.Analysis.PSeries
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.unconditionalstatement and proof · cited by 2,068
- absstatement and proof · cited by 1,814
- Summablestatement and proof · cited by 778
- Int.cast_natCastproof · cited by 393
- abs_of_nonnegproof · cited by 279
- Int.cast_negproof · cited by 224
- Nat.cast_nonnegproof · cited by 109
- abs_negproof · cited by 93
- neg_lt_neg_iffproof · cited by 39
- Summable.of_nat_of_negproof · cited by 6
- Real.summable_nat_rpowproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_inv_of_isBigO_rpow_invproof · cited by 5
- Real.tsum_eq_tsum_fourier_of_rpow_decayproof · cited by 2
- Real.tsum_eq_tsum_fourier_of_rpow_decay_of_summableproof · cited by 1