# elementary function

An is a real function (of one variable) that can be constructed by a finite number of elementary operations (addition, subtraction, multiplication and division) and compositions from constant functions, the identity function ($x\mapsto x$), algebraic functions, exponential functions, logarithm functions, trigonometric functions and cyclometric functions.

Examples

• Consequently, the polynomial functions, the absolute value$|x|=\sqrt{x^{2}}$,  the triangular-wave function$\arcsin(\sin{x})$, the power function$x^{\pi}=e^{\pi\ln{x}}$  and the function$x^{x}=e^{x\ln{x}}$  are elementary functions (N.B., the real power functions entail that  $x>0$).

• $\displaystyle\zeta(x):=\sum_{n=1}^{\infty}\frac{1}{n^{x}}$  and  $\displaystyle\operatorname{Li}{x}:=\int_{2}^{x}\frac{dt}{\ln{t}}$  are not elementary functions — it may be shown that they can not be expressed is such a way which is required in the definition.

Title elementary function ElementaryFunction 2013-03-22 14:46:29 2013-03-22 14:46:29 pahio (2872) pahio (2872) 18 pahio (2872) Definition msc 26A99 RiemannZetaFunction LogarithmicIntegral AlgebraicFunction TableOfMittagLefflerPartialFractionExpansions