Papers › 2-FAST: Fast and accurate computation of projected two-point functions
2-FAST: Fast and accurate computation of projected two-point functions
Henry S. Grasshorn Gebhardt, Donghui Jeong
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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, ξ_ℓ^ν(r), or spherical harmonic space, C_ℓ(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.
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