Theorems · Theorem · number theory
LindemannWeierstrass.integral_exp_mul_eval
∀ (p : Polynomial ℂ) (s : ℂ),
s * ∫ (x : ℝ) in 0..1, Complex.exp (-(x • s)) * Polynomial.eval (x • s) p =
-(Complex.exp (-s) * Polynomial.eval s (Polynomial.sumIDeriv p)) + Polynomial.eval 0 (Polynomial.sumIDeriv p)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- one_smulproof · cited by 1,374
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Polynomial.evalstatement and proof · cited by 796
- zero_smulproof · cited by 716
- Complex.expstatement and proof · cited by 612
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