Theorems · Theorem · sequences and series
HasSum.nat_add_neg_add_one
∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M] {m : M} {f : ℤ → M},
HasSum f m → HasSum (fun n => f ↑n + f (-(↑n + 1))) m- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumproof · cited by 5,195
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Finset.imageproof · cited by 910
- HasSumstatement and proof · cited by 518
- Function.Injective.injOnproof · cited by 280
- Finset.sum_add_distribproof · cited by 131
- Finset.preimageproof · cited by 108
- Finset.mem_imageproof · cited by 105
- Finset.mem_unionproof · cited by 49
Cited by5
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_nat_hurwitzZetaEvenproof · cited by 1
- HurwitzZeta.hasSum_nat_hurwitzZetaOddproof · cited by 1
- PowerSeries.WithPiTopology.hasSum_pow_pentagonal_sub_pentagonalSeriesproof · cited by 1
- tsum_nat_add_neg_add_oneproof · cited by 0
- Summable.nat_add_neg_add_oneproof · cited by 0