| 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.
|
