Beyond the traditional Line-of-Sight approach of cosmological angular statistics

We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count Cℓ's (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear $C_{\ell}'$s. In both cases our approach speeds up the calculation of the exact $C_{\ell}^{\prime}$s (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.