# 2-FAST: Fast and Accurate Computation of Projected Two-point Functions

Research paper by Henry S. Grasshorn Gebhardt, Donghui Jeong

Indexed on: 14 Sep '17Published on: 14 Sep '17Published in: arXiv - Astrophysics - Cosmology and Nongalactic Astrophysics

#### Abstract

We present the 2-FAST (2-point Function from Fast and Accurate Spherical Bessel Transformation) 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. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.