# function stZnAll=GenZnAll(nn_max, rho,sBessel)
# computes the three Zn(rho) auxiliary functions for the radial
# dependence of VSHs for n=1 to nn_max
# can be used for both regular VSHs (based on j(rho)) or
# irregular VSHs (based on h1(rho)).
bessel_z <- function(rho, n_max, type = "h"){
rho <- as.complex(rho)
if(type == "j") {
f <- sq * BesselJ(z = rho, nu = 0.5, nSeq = n_max+1)
} else if(type == "h") {
f <- sq * BesselH(z = rho, nu = 0.5, nSeq = n_max+1, m = 1)
}
sq <- sqrt((pi/2)/rho)
# matrix of spherical Bessel
Zn <- outer(sq, f)
Z0 <- Zn[,2:(nn_max+1)]
Z1 <- outer(Z0, 1/rho)
Z2 <- Zn[,n] - outer(n,Z1)
list(Z0=Z0, Z1=Z1, Z2=Z2)
}
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