21. :What " elementary functions " are allowed? 22. The third elementary function of the center is to set up a small library for relevant material. 23. The arc length of an ellipse, in general, has no closed-form solution in terms of elementary functions . 24. Unfortunately, it's not an inverse that can be written in terms of elementary functions , to my knowledge. 25. As concerns estimations resorting to non-elementary functions and solutions, Knessl, Coffey and Fekih-Ahmed obtained quite accurate results. 26. The Liouvillian functions are defined as the elementary functions and, recursively, the integrals of the Liouvillian functions. 27. It follows directly from the definition that the set of elementary functions is limits and infinite sums. 28. :: But even when the inverse exists, it's not necessarily expressible in terms of " elementary functions ". 29. These integrals cannot be expressed in terms of elementary functions , and are often said to be special functions. 30. In this case, however, it is possible to calculate the integral in closed form using only elementary functions .
