Theorems · Theorem · complex analysis
Complex.hasSum_arctan
∀ {z : ℂ}, ‖z‖ < 1 → HasSum (fun n => (-1) ^ n * z ^ (2 * n + 1) / ↑(2 * n + 1)) z.arctanThe power series expansion of Complex.arctan, valid on the open unit disc.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
Cited by1
Results whose statement or proof uses this declaration.
- Real.hasSum_arctanproof · cited by 1