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      We define the field  of
      logarithmic hyperseries, construct on
 of
      logarithmic hyperseries, construct on  natural operations of differentiation, integration, and composition,
      establish the basic properties of these operations, and characterize
      these operations uniquely by such properties.
      natural operations of differentiation, integration, and composition,
      establish the basic properties of these operations, and characterize
      these operations uniquely by such properties.
    
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