§6   Merlin Transform

 

    The Merlin transform of [ Merlin transform and its inversion formula ]   is

                        

    The inversion formula of Merlin transform is:

                        

    [ Important formula table of Merlin transform ]

 

original function

Merlin transformed function

          

         

        

    

   

, when

   

original function

Merlin transformed function

 

 

    [ Merlin transformation table ]

               

M ( z )

                        ( Re z > 0 )

                        ( Re z < 0 )

                    ( Re z >- Rev )

                  ( Re z < - Rev )

         

                (0 < Re z < 1)

 

                           (0 < Re z < n )

         

                (0 < Re z < 1)

         (Integral in the sense of principal value)

    

  (0 < Re z < 2)

         (Integral in the sense of principal value)

           

  (0 < Re z < 2)

         (Integral in the sense of principal value)

    (Rev > 0)

      ( 0 < Re z < Rev )

 ( Rev > )

            ( Re z > 0 )

 ( Rev > )

    ( Re z < )

          

                    ( Re z > 0 )

             ( Re z > 0 )

                      ( Re z < 0 )

         

  (0 < Re z < 1)

                  (0 < Re z < 1)

                (0 < Re z < 1)

              ( < Re z < 0)

              ( < Re z < 0)

                  ( < Re z < 1)

      (0<Rez < 1)

                           

                ( < Re z < 1)

                           

                ( 0 < Re z < 1)

  

      (Re z > -1)

  

                

 

                 

 

       ( Re z > )

           ( Re z > )

            ( < Re z < 0)

 

 

               (0<Rez < 1)

 

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