AP effect using Gauss-Lobatto Quadrature

[marcobonici]

Actually the AP effect is included in the emulators, for speed purposes. What would be interesting, is the possibility to include the AP effect a posteriori. One useful approach is possibly the Gauss-Lobatto quadrature. In order to finish this issue, we need to write a notebook with:

• The AP effect as evaluated by PyBird
• The AP effect implemented in Julia with the same approach of PyBird
• The AP effect implemented in Julia with QuadGK
• The AP effect implemented using the Gauss-Lobatto quadrature After these tests, the notebook must be uploaded here

[marcobonici]

Tests finished. The results are the following:

• Using the adaptive Gauss-Kronrod quadrature computes the AP effect in about $1\, ms$
• Using the Gauss-Lobatto rule with 8 points gives the result in about $30\,\mu s$
• The percentual difference between GK and GL for the hexadecapole (the less precise one) are of order 1e-5 Adding the developed code in a new branch