Theorems · Theorem · special functions
Complex.tendsto_euler_sin_prod
∀ (z : ℂ),
Filter.Tendsto (fun n => ↑Real.pi * z * ∏ j ∈ Finset.range n, (1 - z ^ 2 / (↑j + 1) ^ 2)) Filter.atTop
(nhds (Complex.sin (↑Real.pi * z)))Euler's infinite product formula for the complex sine function.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Filterproof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Finset.prodstatement and proof · cited by 2,356
- mul_commproof · cited by 2,262
Cited by3
Results whose statement or proof uses this declaration.
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- tendsto_euler_sin_prod'proof · cited by 1
- Real.tendsto_euler_sin_prodproof · cited by 0