11. The family of all step functions evidently satisfies the above axioms for elementary functions . 12. In general, integrals in this form cannot be expressed in terms of elementary functions . 13. He devised the Gal's accurate tables method for the computer evaluation of elementary functions . 14. Interobjects may have an elementary function in human thought. 15. Importantly, the elementary functions are " not " closed under Liouville's theorem, see Nonelementary integral. 16. :The Cumulative distribution function of the Normal distribution does not exist as an elementary function . 17. An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s. 18. Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841.19. However, these numbers are not known to be expressible by themselves in terms of elementary functions . 20. Then all the terms in the asymptotic series can be expressed in terms of elementary functions .
