Fast and accurate computation of projected two-point functions

We present the two-point function from the fast and accurate spherical Bessel transformation (2-FAST) algorithm¹Our code is available at https://github.com/hsgg/twoFAST. 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, ξlν(r), or spherical harmonic space, Cl(χ,χ′). 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. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.