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

Abstract

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, $C_{\ell }(\chi ,{\chi }^{\prime })$. 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.

40 pages, 24 figures

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