Theorems · Theorem · number theory
ModularForm.differentiableOn_tprod_one_sub_pow
DifferentiableOn ℂ (fun q => ∏' (n : ℕ), (1 - q ^ (n + 1))) (Metric.ball 0 1)
The infinite product q ↦ ∏' n, (1 - q^(n+1)) is differentiable on the open unit disc.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetproof · cited by 13,712
- Complexstatement and proof · cited by 5,565
- SummationFilter.unconditionalstatement · cited by 2,068
- Metric.ballstatement and proof · cited by 735
- Finset.prod_congrproof · cited by 646
- Filter.Eventually.of_forallproof · cited by 526
- DifferentiableOnstatement and proof · cited by 419
- tprodstatement · cited by 230
- Metric.isOpen_ballproof · cited by 63
- differentiableOn_idproof · cited by 13
- Finset.prod_fnproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- ModularForm.differentiableAt_eta_tprodproof · cited by 2
- ModularForm.differentiableOn_tprod_one_sub_pow_powproof · cited by 1