Elementary Function
A function built up of compositions of algebraic functions, the Exponential Function and the TrigonometricFunctions and their inverses by Addition, Multiplication, Division, root extractions (theElementary Operations) under repeated compositions (Shanks 1993, p. 145). Unfortunately,there are several different definitions of what constitutes an elementary function.
Following Liouville, Watson (1966, p. 111) defines
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and lets
, etc. These functions are then called elementary, although Watson confusingly terms them``elementary transcendental functions.''Not all functions are elementary. For example, the Normal Distribution Function
is a notorious example of a nonelementary function. The Elliptic Integral
is another. Nonelementary functions are called Transcendental Functions.See also Algebraic Function, Elementary Operation, Elementary Symmetric Function, TranscendentalFunction
References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993. Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, p. 111, 1966.
- Wheel
- Wheel Graph
- Wheel Paradox
- Whewell Equation
- Whipple's Transformation
- Whirl
- Whisker Plot
- Whitehead Double
- Whitehead Link
- Whitehead Manifold
- Whitehead's Theorem
- Whitney-Graustein Theorem
- Whitney-Mikhlin Extension Constants
- Whitney Singularity
- Whitney Sum
- Whitney Umbrella
- Whittaker Differential Equation
- Whittaker Function
- Whole Number
- Width (Partial Order)
- Width (Size)
- Wiedersehen Manifold
- Wieferich Prime
- Wielandt's Theorem
- Wiener Filter