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A common problem in cosmology is to integrate the product of two or morespherical Bessel functions (sBFs) with different configuration-space argumentsagainst the power spectrum or its square, weighted by powers of wavenumber.Naively computing them scales as $N_{\rm g}^{p+1}$ with $p$ the number ofconfiguration space arguments and $N_{\rm g}$ the grid size, and they cannot bedone with Fast Fourier Transforms (FFTs). Here we show that by rewriting thesBFs as sums of products of sine and cosine and then using the product to sumidentities, these integrals can then be performed using 1-D FFTs with $N_{\rmg} \log N_{\rm g}$ scaling. This "rotation" method has the potential toaccelerate significantly a number of calculations in cosmology, such asperturbation theory predictions of loop integrals, higher order correlationfunctions, and analytic templates for correlation function covariance matrices.We implement this approach numerically both in a free-standing,publicly-available \textsc{Python} code and within the larger,publicly-available package \texttt{mcfit}. The rotation method evaluated withdirect integrations already offers a factor of 6-10$\times$ speed-up over thenaive approach in our test cases. Using FFTs, which the rotation methodenables, then further improves this to a speed-up of $\sim$$1000-3000\times$over the naive approach. The rotation method should be useful in light ofupcoming large datasets such as DESI or LSST. In analysing these datasetsrecomputation of these integrals a substantial number of times, for instance toupdate perturbation theory predictions or covariance matrices as the inputlinear power spectrum is changed, will be one piece in a Monte Carlo MarkovChain cosmological parameter search: thus the overall savings from our methodshould be significant.

Rotation method for accelerating multiple-spherical Bessel function integrals against a numerical source function