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Orders of Magnitude: The 0, o, ~ Notation

  • Richard M. Meyer
Part of the Universitext book series (UTX)

Abstract

In many practical applications of Mathematics it is necessary to consider the behavior of some function f(x) of x as x tends to some limit (finite or infinite). However, many times the function f(x) is extremely complicated in nature, or incompletely known, and it is preferable (in fact, perhaps only possible) to describe the asymptotic behavior of f(x) relative to (or compared with) some other function g(x) of x as x tends to the same limit. In practice, the comparison function g is often chosen as a “simpler” function, such as a power or exponential function.

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References to Additional and Related Material: Section 6

  1. 1.
    Abramowitz, M. and I. Stegun (Editors), “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables”, National Bureau of Standards, Applied Mathematics Series No. 55, Washington, D. C. (1964).Google Scholar
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    Lebedev, N., “Special Functions and Their Applications”, Prentice-Hall, Inc. Englewood Cliffs, N.J. (1965).zbMATHGoogle Scholar
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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Richard M. Meyer
    • 1
  1. 1.Niagara University, College of Arts and SciencesNiagara UniversityUSA

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