There is a small mistake (or just rather an inconsistency) in the way you define the c-type Gaunt coefficients in the section about Legendre Polynomials. There is a factor 4_k+1 that should be 2_k+1 to make it consistent with the definition trough the wigner 3-j-s. you simplify by (2_k+1)/(4_k+1) at some point..
Reported by László Oroszlány and Laszlo Szunyogh.
There is a small mistake (or just rather an inconsistency) in the way you define the c-type Gaunt coefficients in the section about Legendre Polynomials. There is a factor 4_k+1 that should be 2_k+1 to make it consistent with the definition trough the wigner 3-j-s. you simplify by (2_k+1)/(4_k+1) at some point..