lcfa.cyl: Calculates the logarithmic derivative of the Cylindrical...

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

Description

Calculates the logarithmic derivative of the Cylindrical Bessel functions.

Usage

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

Arguments

nmax	The maximum order of J_n(x)
x	The argument of the functions. Can be complex.
code	If you prefer to use native R or C language.
NMAX	Maximum number of iterations

Details

lcfa.cyl calculates the logarithmic derivative of Cylindrical Bessel functions D[n]=J_n'/J_n using downward recurrence. The system of equations is given by S_n(x)=n/x, g[n]=J_n/J_{n+1} and D_n=J_n'(x)/J_n(x). The system can be solved by means of the recurrence relations of the Cylindrical Bessel functions

g[n-1]+1/g[n]=2 S[n]

g[n-1]-1/g[n]=2 D[n]

that can be rewriten

g[n]=S[n+1]+D[n+1]

1/g[n]=S[n ]-D[n ].

The logarithmic derivatives obeys the relation,

(S[n]-D[n])(S[n+1]+D[n+1])=1.

The values are calculated by downward recurrence, and the inicial values calculated by Lentz method.

Value

An array of the logarithmic derivative of Cylindrical Bessel functions and the ratio between two consecutive Cylindrical Bessel functions. from 0 to nmax at point x

See Also

lcfe.cbi, lcfe.cbl, lcfe.cbd.

Examples

nmax<-10
x<-5
u.c<-lcfa.cyl(nmax,x,code="C")
u.r<-lcfa.cyl(nmax,x,code="R")
u<-data.frame(
   # Logarithmic Derivatives
   C.LogDev=u.c$Dn,R.LogDev=u.r$Dn,
   # Ratio between Cylindrical Bessel functions
   C.CylRat=u.c$gn,R.CylRat=u.r$gn)
print(u)

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