Theorems · Theorem · number theory
ModularForm.logDeriv_one_sub_mul_cexp_comp
∀ (r : ℂ) {g : ℂ → ℂ},
Differentiable ℂ g →
logDeriv ((fun z => 1 - r * Complex.exp z) ∘ g) = fun z =>
-r * deriv g z * Complex.exp (g z) / (1 - r * Complex.exp (g z))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- derivstatement and proof · cited by 676
- Complex.expstatement and proof · cited by 612
- Differentiablestatement and proof · cited by 298
- logDerivstatement · cited by 71
- differentiableAt_idproof · cited by 63
- DifferentiableAt.const_subproof · cited by 14
- DifferentiableAt.const_mulproof · cited by 12
- DifferentiableAt.cexpproof · cited by 4
- logDeriv_compproof · cited by 3
- ModularForm.logDeriv_one_sub_cexpproof · cited by 1
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