1\name{BernoulliQ} 2\alias{BernoulliQ} 3\title{Exact Bernoulli Numbers} 4\description{%% ../R/Stirling-n-etc.R : 5 Return the \eqn{n}-th Bernoulli number \eqn{B_n}, (or \eqn{B_n^+}{Bn+}, 6 see the reference), where \eqn{B_1 = + \frac 1 2}{B_1 = + 1/2}. 7} 8\usage{ 9BernoulliQ(n, verbose = getOption("verbose", FALSE)) 10} 11\arguments{ 12 \item{n}{integer \emph{vector}, \eqn{n \ge 0}{n >= 0}.} 13 \item{verbose}{logical indicating if computation should be traced.} 14} 15\value{ 16 a big rational (class \code{\link[=bigq-class]{"bigq"}}) vector of the 17 Bernoulli numbers \eqn{B_n}. 18} 19\references{\url{https://en.wikipedia.org/wiki/Bernoulli_number} 20} 21\author{Martin Maechler} 22\seealso{ 23 \code{\link[Rmpfr]{Bernoulli}} in \CRANpkg{Rmpfr} in arbitrary precision 24 via Riemann's \eqn{\zeta}{zeta} function. 25 % \code{\link[DPQ]{Bern}(n)} 26 \code{Bern(n)} in \CRANpkg{DPQ} uses standard (double precision) 27 \R arithmetic for the n-th Bernoulli number. 28} 29\examples{ 30(Bn0.10 <- BernoulliQ(0:10)) 31} 32