2-FAST: Fast and accurate computation of projected two-point functions

Understand

We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions.

• These types of integrals occur when projecting the galaxy power spectrum $P(k)$ onto the configuration space, $\xi_\ell^\nu(r)$, or spherical harmonic space, $C_\ell(\chi,\chi')$.
• First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions.
• We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation.