Good morning, I have been asking myself the kind of differential equation obtained by modifying the radial solution Rl(rho)=Al jl(rho)+Bl neumann l(rho) Eq.1. analyzed from the Helmholtz equation where the Bessel kind Jl+1/2(rho), l=0, 1, 2,.... is used through the spherical Bessel function jl(rho), what it would be the new expression below

Rl(rho)= rhol Al jl(rho)+rhol Bl neumannl(rho). Eq(2).

and rho is the spherical coordínate rho . My concern is to find a differential equation that’s satisfied by Eq(2) for any variation of the classical Helmholtz‘s . My concern is to define a sum over l=0, 1, 2,....infinite, of the sum {Alnl jl(n) } which is a combination of spherical Bessel functions j_l(n), rho=n=1, 2,... where Al is defined by me as (1/l! )4l(-1)l