lcfa.ric: Array of logarithmic derivative and ratio of Ricatti-Bessel...

In wendellopes/rvswf: RVSWF: Expansion in Vector Spherical Wave Functions written in R

Description

Array of logarithmic derivative and ratio of Ricatti-Bessel functions.

Usage

lcfa.ric(nmax, x, code = "C", NMAX = 200)

Arguments

nmax	Maximun value of n.
x	The argument of the functions. Can be complex.
code	If the C code or R built in.
NMAX	Maximum number of iterations on the Lentz algorithm.

Details

Calculate by downward recurrence the derivative of Ricatti-Bessel functions C_n=ψ_n'(x)/ψ_n(x), where ψ_n(x)=xj_n(x), and simultaneously the ratio ρ_n=ψ_n(x)/ψ_{n+1}(x)=j_n(x)/j_{n+1}(x), from 0 to nmax. The starting values are calculated by Lentz continued fraction method.

See Also

lcfe.rbl, lcfe.sbd, lcfe.sbi.

Examples

nmax<-10
x<-5
u.c<-lcfa.ric(nmax,x,code="C")
u.r<-lcfa.ric(nmax,x,code="R")
u<-data.frame(
   # Logarithmic Derivatives
   C.LogDev=u.c$Cn,R.LogDev=u.r$Cn,
   # Ratio between Ricatti-Bessel functions
   C.RicRat=u.c$rn,R.RicRat=u.r$rn)
print(u)

wendellopes/rvswf documentation built on May 4, 2019, 4:19 a.m.