In addition to the default Legendre basis, it would be nice to select Cosine basis for calculations. The orthonormal cosine basis is defined as follows:
$$
\varphi_k(x) = \sqrt{\frac{1}{b_k-a_k} \frac{8\pi k}{\sin 4\pi k + 4\pi k}}\cos(2\pi k \frac{x - a_k}{b_k-a_k})
$$
The user will now have two options for orthonormal basis: "Legendre" and "Cosine".
In addition to the default Legendre basis, it would be nice to select Cosine basis for calculations. The orthonormal cosine basis is defined as follows:
$$ \varphi_k(x) = \sqrt{\frac{1}{b_k-a_k} \frac{8\pi k}{\sin 4\pi k + 4\pi k}}\cos(2\pi k \frac{x - a_k}{b_k-a_k}) $$
The user will now have two options for orthonormal basis: "Legendre" and "Cosine".
The validation of the new cosine basis is here.