OAI/MathematicalPhysics/DefocusingNLS/Profile/SlowEulerEquation.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

Integration by parts for the confluent hypergeometric equation

  1. def OAI.DefocusingNLS.slowEulerPrimitive line 12
  2. def OAI.DefocusingNLS.slowEulerBoundaryDerivative line 15
  3. theorem OAI.DefocusingNLS.hasDerivAt_slowEulerPrimitive line 20
  4. theorem OAI.DefocusingNLS.slowEulerPrimitive_eq_kernel line 62
  5. theorem OAI.DefocusingNLS.integrable_slowEulerBoundaryDerivative line 68
  6. theorem OAI.DefocusingNLS.integral_slowEulerBoundaryDerivative line 77
  7. theorem OAI.DefocusingNLS.slowEuler_integral_relation line 102

    Source documentation

    The integral identity underlying Kummer's equation.

    theorem slowEuler_integral_relation (q : ℂ) (m : ℕ) (x : ℂ)
    (hq : 0 < q.re) (hx : 0 < x.re) :
    x * (∫ v : ℝ in Set.Ioi 0, slowEulerKernel (q + 2) (m + 2) x v) +
      (x - (m : ℂ)) * (∫ v : ℝ in Set.Ioi 0, slowEulerKernel (q + 1) (m + 1) x v) -
      q * (∫ v : ℝ in Set.Ioi 0, slowEulerKernel q m x v) = 0 := by
…

    Mentions: OAI.DefocusingNLS.slowEulerKernel