Essential Mathematics for Applied Fields pp 181-190 | Cite as

# Orders of Magnitude: The 0, o, ~ Notation

Chapter

## 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

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- 4.Cramér, H., “Mathematical Methods of Statistics”, Princeton University Press (1958).Google Scholar
- 5.Hobson, E., “Theory of Functions of a Real Variable”, Vol. II, Dover Publications, New York.Google Scholar
- 6.Lebedev, N., “Special Functions and Their Applications”, Prentice-Hall, Inc. Englewood Cliffs, N.J. (1965).zbMATHGoogle Scholar
- 7.Pearson, K., (Editor), “Tables of the Incomplete Gamma Function”, London (1922).Google Scholar
- 8.Richardson, C., “An Introduction to the Calculus of Finite Differences”, Van Nostrand, Inc., New York (1954).zbMATHGoogle Scholar
- 9.Spiegel, M., “Mathematical Handbook of Formulas and Tables”, Schaum’s Outline Series, Schaum Publishing Co., New York (1968).Google Scholar
- 10.Whittaker, E. and G. Watson, “A Course in Modern Analysis”, Cambridge University Press (1952).Google Scholar

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