Theorems · Theorem · real analysis
integral_exp_mul_complex
∀ {a b : ℝ} {c : ℂ}, c ≠ 0 → ∫ (x : ℝ) in a..b, Complex.exp (c * ↑x) = (Complex.exp (c * ↑b) - Complex.exp (c * ↑a)) / c- Cited by
- 2 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
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- AddCommGroupproof · cited by 12,871
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- Complexstatement and proof · cited by 5,565
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- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- ContinuousSMulproof · cited by 1,016
- Complex.expstatement and proof · cited by 612
- intervalIntegralstatement · cited by 546
Cited by2
Results whose statement or proof uses this declaration.
- integral_exp_mul_complex_Ioiproof · cited by 2
- integral_exp_mul_I_eq_sinproof · cited by 1