Theorems · Theorem · special functions
Complex.tendsto_self_mul_Gamma_nhds_zero
Filter.Tendsto (fun z => z * Complex.Gamma z) (nhdsWithin 0 {0}ᶜ) (nhds 1)At s = 0, the Gamma function has a simple pole with residue 1.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterproof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- zero_addproof · cited by 2,366
- nhdsWithinstatement and proof · cited by 1,912
- ContinuousAtproof · cited by 697
- Continuous.continuousAtproof · cited by 297
- Complex.Gammastatement and proof · cited by 96
- ContinuousAt.comp'proof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Complex.not_continuousAt_Gamma_zeroproof · cited by 2
- Complex.Gammaℝ_residue_zeroproof · cited by 1