lgammaAsymp: Asymptotic Log Gamma Function

In DPQ: Density, Probability, Quantile ('DPQ') Computations

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

lgamma.

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
  }

DPQ documentation built on Dec. 5, 2023, 3:05 a.m.