Theorems · Definition · real analysis
Real.arsinh
ℝ → ℝ
arsinh is defined using a logarithm, arsinh x = log (x + √(1 + x^2)).
- Defined in
- Mathlib.Analysis.SpecialFunctions.Arsinh
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by56
Results whose statement or proof uses this declaration.
- Real.sinh_arsinhstatement and proof · cited by 8
- Real.contDiff_arsinhstatement · cited by 6
- UpperHalfPlane.sinh_half_distproof · cited by 6
- Real.hasDerivAt_arsinhstatement · cited by 5
- Real.sinhEquivproof · cited by 5
- Real.hasStrictDerivAt_arsinhstatement and proof · cited by 3
- Real.differentiable_arsinhstatement · cited by 3
- Real.cosh_arsinhstatement and proof · cited by 2
- UpperHalfPlane.dist_eqstatement · cited by 2
- Real.arsinh_injectivestatement · cited by 2
- Filter.Tendsto.arsinhstatement · cited by 2
- Real.exp_arsinhstatement · cited by 2