Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: III integral
An exponent extension is implemented to the computation of the integrals of fnALF. The exponent extension is dynamically terminated during the increasing-degree recursions. The sectorial integrals are correctly computed by the forward recursion only. The extended subroutines can compute integrals of arbitrary high degree/order quickly. The extended subroutines are provided as the attached computer codes.
exponent extension forward recursion integral of associated legendre functions spherical harmonic analysis underflow problem