• J. Kevorkian
  • J. D. Cole
Part of the Applied Mathematical Sciences book series (AMS, volume 34)


We will use the conventional order symbols as a mathematical measure of the relative order of magnitude of various quantities. Although generalizations are straightforward, we need only be concerned with scalar functions of real variables. In the definitions which follow φ, ψ, etc. are scalar functions of the variable x (which may be a vector) and the scalar parameter ε. The variable x ranges over some domain D and ε belongs to some interval I.


Asymptotic Expansion Limit Process Remainder Term Lower Order Term Direct Match 
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  1. 1.1.1
    A. Erdelyi, Asymptotic Expansions, Dover Publications, New York, 1956.Google Scholar
  2. 1.2.1
    G. F. Carrier. M. Krook and C. E. Pearson, Functions of a Complex Variable, Theory and Technique, McGraw-Hill Book Company, New York, 1966.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Kevorkian
    • 1
  • J. D. Cole
    • 2
  1. 1.Applied Mathematics ProgramUniversity of WashingtonSeattleUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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