Timetable

During this first period I searched for the bugs related to special functions in the bug tracker. I found these four bugs that need to be fixed:

1. gammainc: the upper version rounds down to zero if the output is small. For this bug there is a lot of work already done by Marco and Nir. I will just fix the last few things (like the input validation).
2. gammaincinv: after finishing gammainc, I should start working on the inverse (which is missing in Octave).
3. betainc: it is necessary to fix the input validation.
4. besselj: it gives NaN if the input is too large. Actually, also other versions of the Bessel function have the same problem.

My idea of the timetable is the following

• First part (May 30 - June 26: 4 weeks):
  • 1st week: finish to fix gammainc (input validation, documentation, add tests)
  • 2nd and 3rd weeks: write gammaincinv (via Newton's method)
  • 4th week: fix the input validation for betainc (and, if needed, add tests and fix the documentation)
• Second part (July 1 - July 24: 3 weeks): fix the Bessel functions. Some ideas comprehend to test other libraries in addition to the amos (which is the library currently in use) and try to implement new algorithms. Add tests and revise the documentation.
• Final part (July 29 - August 21: 3 weeks): add tests to the other special functions to make sure they work properly, trying to fix the problems that, eventually, will be found and revise the documentation if needed.