Theorems · Theorem · sequences and series
tsum_int_eq_zero_add_two_mul_tsum_pnat
∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : UniformSpace G] [IsUniformAddGroup G] [CompleteSpace G] [T2Space G]
{f : ℤ → G}, Function.Even f → Summable f → ∑' (n : ℤ), f n = f 0 + 2 • ∑' (n : ℕ+), f ↑↑n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- T2Spacestatement and proof · cited by 1,351
- tsumstatement and proof · cited by 1,148
- Summablestatement and proof · cited by 778
- add_assocproof · cited by 746
- PNatstatement and proof · cited by 392
- IsUniformAddGroupstatement and proof · cited by 342
- PNat.valstatement and proof · cited by 226
- two_nsmulproof · cited by 67
Cited by2
Results whose statement or proof uses this declaration.
- two_mul_riemannZeta_eq_tsum_int_inv_pow_of_evenproof · cited by 2
- tsum_eisSummand_eq_tsum_sigma_mul_cexp_powproof · cited by 1