Elementary Function

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elementary function

[‚el·ə′men·trē ′fəŋk·shən]
Any function which can be formed from algebraic functions and the exponential, logarithmic, and trigonometric functions by a finite number of operations consisting of addition, subtraction, multiplication, division, and composition of functions.

Elementary Function


any function in the class consisting of polynomials, rational functions, exponential functions, logarithmic functions, trigonometric functions, and inverse trigonometric functions. The class of elementary functions also includes functions obtained from those listed above through the performance of the four arithmetic operations and composition (the formation of a composite function) a finite number of times; examples are

The class of elementary functions has been best studied, and is most often encountered, in applications of mathematics. Many practical problems, however, lead to the consideration of functions that are not elementary functions, such as cylindrical functions. The derivative of an elementary function is also an elementary function. The indefinite integral of an elementary function is not always expressed in terms of an elementary function. Nonelementary functions are often represented in terms of elementary functions through the use of, for example, infinite series, infinite products, and infinite integrals.

References in periodicals archive ?
The combination of the previous elementary functions with elementary parameters was used to calculate the RTD function of the various combinations according to Eq.
Representing an image with a few elementary functions is widely used in image processing and computer vision.
It is obvious that the term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ds can not solved directly due to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ds can not be expressed by elementary functions.
For those elementary functions demonstrated in Examples 1 through 4, we have seen that in order to make [absolute value of r(x,h)] as small as we wish, it will be easier if [absolute value of r(x,h)] can be bounded above by C[absolute value of h], where C is a constant.
For non-monotonic elementary functions, such as the trigonometric functions, algorithmic definitions are still easily obtained.
In this paper a slightly modification is proposed to the original Wong and Goto's ATA method for the computation of elementary functions in IEEE 754 single precision.
For that reason, the idea of the Gabor expansion is to express a signal S(k) as a weighted summation of elementary functions formed from Gaussian weighted complex exponentials that exhibit a corresponding Gaussian-shaped spectrum.
They were also less proficient at the tasks of basic calculus, such as differentiating and integrating elementary functions.
Automatic differentiation is based on the fact that all computer programs, no matter how complicated, use a finite set of elementary functions as defined by the programming language.
Those who actually manage to register have reported difficulties with elementary functions such as sending email and web browsing.
These are arranged in sessions each focused on a specific objective, among then elementary functions and differential, Cauchy integral formula, and contour integration.
It is easy to draw images of lines and circles for the most elementary functions, but other objects can get complicated very quickly.