Theorems · Theorem · sequences and series
summable_norm_pow_mul_geometric_of_norm_lt_one
∀ {R : Type u_4} [inst : NormedRing R] (k : ℕ) {r : R}, ‖r‖ < 1 → Summable fun n => ‖↑n ^ k * r ^ n‖- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Filter.atTopproof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- NormedRingstatement and proof · cited by 924
- Summablestatement and proof · cited by 778
- Asymptotics.isBigO_reflproof · cited by 51
- summable_norm_mul_geometric_of_norm_lt_oneproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_sigma_mul_cexp_powproof · cited by 2
- summable_norm_pow_mul_geometric_div_one_subproof · cited by 1
- summable_norm_geometric_of_norm_lt_oneproof · cited by 1