Lerch's Contribution to the Theory of Analytic Functions
The relationship between continuity,differentiability and analysis of functions is an important subject in mathematics during the 19th century.M.Lerch is an important researcher in the development of this problem from mathematical cases to general theories,and is the mathematician with the most relevant literatures in this period.Based on the original literature,this paper systematically analyzes Lerch's working background,thinking methods and important influence on this problem for the first time.On the basis of the work of K.Weierstrass and P.du Bois-Reymond,Lerch deeply discussed the continuous non differentiable function,the validity of function expansion into Taylor's series,and the domain of function existence,making the most direct impact on the work of A.Pring-sheim and E.Borel.
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