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Analytic expressions for integrals of products of spherical Bessel functions. (English) Zbl 0736.33004
Authors’ summary: Integrals of several spherical Bessel functions occur frequently in nuclear physics. They are difficult to evaluate using standard numerical techniques because of the slowly decreasing oscillatory form of the integrand. We derive an analytic expression for the infinite integral of three spherical Bessel functions. We then use this result, together with the closure relation for spherical Bessel functions, to show how in principle one can derive an analytic expression for the integral of any number of spherical Bessel functions. We demonstrate this by deriving an analytic expression for the integral of the product of four Bessel functions. As with all these analytic formulae our results require that all angular momenta corresponding to the spherical Bessel function can be coupled together to give an overall scalar quantity and conserve parity. We discuss the numerical accuracy and stability of this procedure.

##### MSC:
 33C10 Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$
##### Keywords:
integrals of products of Bessel functions