OAI/Analysis/FreeEntropy/GaussianHermite.lean

GitHub source file

21 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.FiniteEntropySeparation.realHermite line 9
  2. theorem OAI.FiniteEntropySeparation.realHermite_zero line 10
  3. theorem OAI.FiniteEntropySeparation.realHermite_succ line 11
  4. theorem OAI.FiniteEntropySeparation.realHermite_derivative line 13
  5. theorem OAI.FiniteEntropySeparation.realHermite_monic line 22
  6. theorem OAI.FiniteEntropySeparation.realHermite_degree line 23
  7. def OAI.FiniteEntropySeparation.hermiteSequence line 25
  8. def OAI.FiniteEntropySeparation.hermiteBasis line 26
  9. theorem OAI.FiniteEntropySeparation.hermiteBasis_apply line 29
  10. def OAI.FiniteEntropySeparation.gaussianPolyIntegral line 31
  11. theorem OAI.FiniteEntropySeparation.gaussianPolyIntegral_add line 32
  12. theorem OAI.FiniteEntropySeparation.gaussianPolyIntegral_sub line 36
  13. theorem OAI.FiniteEntropySeparation.gaussianPolyIntegral_smul line 40
  14. theorem OAI.FiniteEntropySeparation.gaussianPolyIntegral_one line 43
  15. theorem OAI.FiniteEntropySeparation.gaussianPolyIntegral_zero line 44
  16. theorem OAI.FiniteEntropySeparation.hermite_raising_lowering line 45
  17. theorem OAI.FiniteEntropySeparation.realHermite_mean line 54
  18. theorem OAI.FiniteEntropySeparation.realHermite_inner line 58
  19. def OAI.FiniteEntropySeparation.gaussianPolyLinear line 70
  20. theorem OAI.FiniteEntropySeparation.hermite_expansion line 74
  21. theorem OAI.FiniteEntropySeparation.hermite_sum_inner line 76