#' Checks the results of Lentz method and internal R Bessel function
#'
#' @details In order to check the results of Lentz method for calculation
#' of Ricatti-Bessel logarithmic derivative \eqn{D_n}.
#' @param n Order of the logarithmic derivative given by \eqn{c_n=\psi_n'/\psi_n},
#' where \eqn{\psi_n=xj_n(x)}.
#' @param x Argument of Bessel functions.
#' @param code If C or native R function.
#' @return Data frame with the values calculated by the algorithm.
#' @seealso \code{\link{lcfe.cbi}}, \code{\link{lcfe.cbl}},
#' \code{\link{lcfe.afs}}, \code{\link{besselJ}}.
#' @include reff.rdj.r reff.rjn.r lcfe.rbl.r lcfe.afs.r
#' @export
#' @examples
#' comp.rbl(5,4,code="C")
#' comp.rbl(5,4,code="R")
comp.rbl<-function(n,x,code="C"){
#------------------------------------
# Riccati Bessel Function
# (S_{n+1}-C_n)(S_{n+1}+C_{n+1})=1
# S_n=n/x
# D_n=(x j_n(x))'/(x j_n(x))
# S_n=lcfe.afs(n,x)
# C_n=lcfe.rbl(n,x)
#------------------------------------
a<-reff.rdj(x,n )/reff.rjn(x,n )
b<-reff.rdj(x,n+1)/reff.rjn(x,n+1)
c<-lcfe.rbl(n ,x,code=code)
d<-lcfe.rbl(n+1,x,code=code)
e<-lcfe.afs(n+1,x)
f<-lcfe.afs(n+1,x)
g<-(n+1)/x
h<-(n+1)/x
#------------------------------------
cat("a<-reff.rdj(x,n )/reff.rjn(x,n )\n")
cat("b<-reff.rdj(x,n+1)/reff.rjn(x,n+1)\n")
cat("c<-lcfe.rbl(n ,x) \n")
cat("d<-lcfe.rbl(n+1,x) \n")
cat("e<-lcfe.afs(n ,x) \n")
cat("f<-lcfe.afs(n+1,x) \n")
#------------------------------------
names=c("C_{n }", # a,c
"C_{n+1}", # b,d
"S_{n+1}", # g,e
"S_{n+1}", # h,f
"1") # 1
v.ref=c(a,b,g,h,(g-a)*(h+b)) #
v.cal=c(c,d,e,f,(e-c)*(f+d)) #
return(cbind(names,v.ref,v.cal))
}
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