Theorems · Theorem · number theory
summable_norm_pow_mul_geometric_div_one_sub
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] (k : ℕ) {r : 𝕜},
‖r‖ < 1 → Summable fun n => ↑n ^ k * r ^ n / (1 - r ^ n)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- sub_zeroproof · cited by 938
- Summablestatement and proof · cited by 778
- tendsto_const_nhdsproof · cited by 330
- norm_mulproof · cited by 171
- norm_powproof · cited by 106
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.summable_logDeriv_one_sub_eta_qproof · cited by 1