For values of m > 5 the accuracy consistently decreases

[JustWhit3]

For values of the quantum number m > 5, the value of the computed coefficients start to decrease consistently. This is due to the fact that to compute the Legendre functions a custom derivative formula is used (see here). This formula is unstable and not very efficient. A way to solve this would be to replace the Legendre functions formula with a another kind of formula.