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We present the 2-point function from Fast and Accurate Spherical BesselTransformation (2-FAST) algorithm for a fast and accurate computation ofintegrals involving one or two spherical Bessel functions. These types ofintegrals occur when projecting the galaxy power spectrum $P(k)$ onto theconfiguration space, $\xi_\ell^\nu(r)$, or spherical harmonic space,$C_\ell(\chi,\chi')$. First, we employ the FFTlog transformation of the powerspectrum to divide the calculation into $P(k)$-dependent coefficients and$P(k)$-independent integrations of basis functions multiplied by sphericalBessel functions. We find analytical expressions for the latter integrals interms of special functions, for which recursion provides a fast and accurateevaluation. The algorithm, therefore, circumvents direct integration of highlyoscillating spherical Bessel functions.

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