Elementary exact evaluation of infinite integrals of the product of several spherical Bessel functions, power and exponential

Fabrikant, V. I.

doi:10.1090/s0033-569x-2012-01300-8

Cited by 17 publications

(11 citation statements)

References 11 publications

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“…×F l + 1, 1 2 ; l + 3 2 ; r r1 2 (66) using j l (x) = π/(2x)J l+1/2 (x) and Gradshteyn & Ryzhik (2007) equation ( 6.512.1). F is the hypergeometric function and we assume r < r1; the result for r > r1 is given by switching r1 ↔ r. f l 2 ll can be computed using techniques outlined in Fabrikant (2013) and is given by his equation ( 9); since the expression is rather long we do not reproduce it here. We mention this since one could imagine scenarios in which high speed was desirable for computing the covariance, such that these approximate forms might suffice.…”

Section: Projection Onto Legendre Polynomialsmentioning

confidence: 99%

Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time

Slepian¹,

Eisenstein²

2015

Mon. Not. R. Astron. Soc.

103

188

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We present an algorithm that computes the multipole coefficients of the galaxy threepoint correlation function (3PCF) without explicitly considering triplets of galaxies. Rather, centering on each galaxy in the survey, it expands the radially-binned density field in spherical harmonics and combines these to form the multipoles without ever requiring the relative angle between a pair about the central. This approach scales with number and number density in the same way as the two-point correlation function, allowing runtimes that are comparable, and 500 times faster than a naive triplet count. It is exact in angle and easily handles edge correction. We demonstrate the algorithm on the LasDamas SDSS-DR7 mock catalogs, computing an edge corrected 3PCF out to 90 Mpc/h in under an hour on modest computing resources. We expect this algorithm will render it possible to obtain the large-scale 3PCF for upcoming surveys such as Euclid, LSST, and DESI.

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Section: Projection Onto Legendre Polynomialsmentioning

confidence: 99%

Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time

Slepian¹,

Eisenstein²

2015

Mon. Not. R. Astron. Soc.

103

188

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“…To this end we apply the method outlined in Ref. [57] and obtain after some analytical simplifications the following expressions. They are checked against their numerical counterparts for different values of m, k a , and k b .…”

Section: Semi-analytical Edf Expressionsmentioning

confidence: 99%

Comparing different density-matrix expansions for long-range pion exchange

Pérez

Bogner

et al. 2021

Phys. Rev. C

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Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. Here we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.

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“…where we define (8.15) This can be computed analytically, following the prescription of Mehrem (2009) and Fabrikant (2013).…”

Section: Bb Termmentioning

confidence: 99%

A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time

Philcox

2020

Preprint

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We present O(N 2 ) estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, halos or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogs. By working in configuration-space, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger k, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shot-noise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, HIPSTER, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of highresolution simulations.

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Elementary exact evaluation of infinite integrals of the product of several spherical Bessel functions, power and exponential

Cited by 17 publications

References 11 publications

Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time

Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time

Comparing different density-matrix expansions for long-range pion exchange

A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time

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