Remainder Cesaro summation incorporates geometric location of terms, is invariant under dilation and scaling, and yields a natural definition of the Gamma function whose properties emerge directly from the definition.
Ahlfors,Complex Analysis: An Introduction to the Theory of Ana- lytic Functions of One Complex Variable, Third Edition, McGraw-Hill
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Introduction to generalised Cesaro convergence II
Remainder Cesaro summation incorporates geometric location of terms, is invariant under dilation and scaling, and yields a natural definition of the Gamma function whose properties emerge directly from the definition.