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Difference between revisions of "Elementary functions"

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The class of functions consisting of the polynomials (cf. [[Polynomial|Polynomial]]), the exponential functions (cf. [[Exponential function, real|Exponential function, real]]), the logarithmic functions (cf. [[Logarithmic function|Logarithmic function]]), the [[Trigonometric functions|trigonometric functions]], the [[Inverse trigonometric functions|inverse trigonometric functions]], and the functions obtained from those listed by the four arithmetic operations and by superposition (formation of a [[Composite function|composite function]]), applied finitely many times. The class of elementary functions is very well studied and occurs most frequently in mathematics. However, many problems lead to the examination of functions that are not elementary (see, for example, [[Special functions|Special functions]]). The derivative of an elementary function is also elementary; the indefinite integral of an elementary function cannot always be expressed in terms of elementary functions. In the study of non-elementary functions one tries to represent these in terms of elementary functions by means of infinite series or products, etc.
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The class of functions consisting of the [[Polynomial|polynomials]], the [[Exponential function, real|exponential functions]], the [[Logarithmic function|logarithmic functions]], the [[Trigonometric functions|trigonometric functions]], the [[Inverse trigonometric functions|inverse trigonometric functions]], and the functions obtained from those listed by the four arithmetic operations and by superposition (formation of a [[Composite function|composite function]]), applied finitely many times. The class of elementary functions is very well studied and occurs most frequently in mathematics. However, many problems lead to the examination of functions that are not elementary (see, for example, [[Special functions|Special functions]]). The derivative of an elementary function is also elementary; the indefinite integral of an elementary function cannot always be expressed in terms of elementary functions. In the study of non-elementary functions one tries to represent these in terms of elementary functions by means of infinite series or products, etc.

Latest revision as of 17:13, 4 May 2012

2010 Mathematics Subject Classification: Primary: 26A09 [MSN][ZBL]

The class of functions consisting of the polynomials, the exponential functions, the logarithmic functions, the trigonometric functions, the inverse trigonometric functions, and the functions obtained from those listed by the four arithmetic operations and by superposition (formation of a composite function), applied finitely many times. The class of elementary functions is very well studied and occurs most frequently in mathematics. However, many problems lead to the examination of functions that are not elementary (see, for example, Special functions). The derivative of an elementary function is also elementary; the indefinite integral of an elementary function cannot always be expressed in terms of elementary functions. In the study of non-elementary functions one tries to represent these in terms of elementary functions by means of infinite series or products, etc.

How to Cite This Entry:
Elementary functions. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Elementary_functions&oldid=25985
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article