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Strlng2=function(n,k,log=TRUE){
# Kaynaklar:
# W W Bleick and Peter C. C. Wang, Asymptotics of Stirling Numbers of the Second Kind,
# Proceedings of the American Mathematical Society Vol. 42, No. 2 (Feb., 1974), pp. 575-580
# N M Temme, Asymptotic Estimates of Stirling Numbers, STUDIES IN APPLIED MATHEMATICS,
# 89:233-243 (1993), Elsevier Science Publicshing.
# This function requires the R package: LamberW.
if (k==1){
topl=1
}else{
z=1:n
nu=n/k
r=1:(n-k)
G=-W(-nu*exp(-nu))
topl=log(sqrt(n-k))+(n-k)*log((n-k)/exp(1))+
(sum(log(z))-sum(log(r))-sum(log(1:k)))-log(sqrt(n*(1-G)))-k*log(G)-(n-k)*log(nu-G)
}
if (log==FALSE){
topl=exp(Rmpfr::mpfr(topl,250))
}
return(Stirling.num=topl)
}
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