which regular solutions for positive energies are given by so-called Bessel functions of the first kind' J l + 1 / 2 ( ρ ) {\displaystyle J_{l+1/2}(\rho )} so that the solutions written for R are the so-called Spherical Bessel function R ( r ) = j l ( k r ) = d e f π / ( 2 k r ) J l + 1 / 2 ( k r ) {\displaystyle R(r)=j_{l}(kr)\ {\stackrel {\mathrm {def} }{=}}\ {\sqrt {\pi /(2kr)}}J_{l+1/2}(kr)} .