Theorems · Definition · difference equations
fwdDiff
{M : Type u_1} → {G : Type u_2} → [AddCommMonoid M] → [AddCommGroup G] → M → (M → G) → M → GForward difference operator, fwdDiff h f n = f (n + h) - f n. The notation Δ_[h] for this
operator is available in the fwdDiff namespace.
- Defined in
- Mathlib.Algebra.Group.ForwardDiff
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddCommMonoidAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- AddCommMonoidstatement and proof · cited by 12,281
Cited by37
Results whose statement or proof uses this declaration.
- fwdDiff_aux.fwdDiffₗproof · cited by 8
- fwdDiff_iter_eq_sum_shiftstatement · cited by 5
- fwdDiff_iter_finsetSumstatement · cited by 5
- fwdDiff_iter_const_smulstatement and proof · cited by 4
- fwdDiff_iter_pow_eq_zero_of_ltstatement and proof · cited by 3
- fwdDiff_aux.coe_fwdDiffₗstatement · cited by 2
- fwdDiff_aux.coe_fwdDiffₗ_powstatement and proof · cited by 2
- PadicInt.fwdDiff_tendsto_zerostatement and proof · cited by 2
- fwdDiff_conststatement · cited by 2
- PadicInt.mahlerEquivproof · cited by 2
- shift_eq_sum_fwdDiff_iterstatement and proof · cited by 1
- IsUltrametricDist.norm_fwdDiff_iter_apply_lestatement · cited by 1