lgammaAsymp {DPQ} | R Documentation |
Asymptotic Log Gamma Function
Description
Compute an n-th order asymptotic approximation to log Gamma function,
using Bernoulli numbers Bern(k)
for k
in
1, \ldots, 2n
.
Usage
lgammaAsymp(x, n)
Arguments
x |
numeric vector |
n |
integer specifying the approximation order. |
Value
numeric vector with the same attributes (length()
etc) as
x
, containing approximate lgamma(x)
values.
Author(s)
Martin Maechler
See Also
Examples
##---- Should be DIRECTLY executable !! ----
##-- ==> Define data, use random,
##-- or do help(data=index) for the standard data sets.
## The function is currently defined as
function (x, n)
{
s <- (x - 1/2) * log(x) - x + log(2 * pi)/2
if (n >= 1) {
Ix2 <- 1/(x * x)
k <- 1:n
Bern(2 * n)
Bf <- rev(.bernoulliEnv$.Bern[k]/(2 * k * (2 * k - 1)))
bsum <- Bf[1]
for (i in k[-1]) bsum <- Bf[i] + bsum * Ix2
s + bsum/x
}
else s
}
[Package DPQ version 0.5-8 Index]