Uniform computational complexity of Taylor series

  • N.Th. Müller
Algorithms And Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


The close connection between an analytic real function and its Taylor series is studied in terms of computational complexity. As central result, the function is computable in polynomial time if and only if the coefficients of the series are uniformly computable in polynomial time. In consequence, integration and analytic continuation of polynomial time computable analytic functions again lead to polynomial time computable functions.


Polynomial Time Taylor Series Analytic Continuation Turing Machine Regular Function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • N.Th. Müller
    • 1
  1. 1.LG Theoretische Informatik Fern Universität HagenHagen

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