Small-angle　x-ray　scattering　(SAXS)　is　an　experimental　biophysical　method　used　for　gaining　insight　into　the　structure　of　large　biomolecular　complexes.　Under　appropriate　chemical　conditions,　the　information　obtained　from　a　SAXS　experiment　can　be　equated　to　the　pair　distribution　function,　which　is　the　distribution　of　distances　between　every　pair　of　points　in　the　complex.　Here　we　develop　a　mathematical　model　to　calculate　the　pair　distribution　function　for　a　structure　of　known　density,　and　analyze　the　computational　complexity　of　these　calculations.　Efficient　recursive　computation　of　this　forward　model　is　an　important　step　in　solving　the　inverse　problem　of　recovering　the　three-dimensional　density　of　biomolecular　structures　from　their　pair　distribution　functions.　In　particular,　we　show　that　integrals　of　products　of　three　spherical-Bessel　functions　arise　naturally　in　this　context.　We　then　develop　an　algorithm　for　the　efficient　recursive　computation　of　these　integrals.　©　Copyright　2015,　Mary　Ann　Liebert,　Inc.　2015.