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integrate lgamma from 0 to Inf

4 messages · Andreas Wittmann, Stavros Macrakis, JLucke at ria.buffalo.edu

Andreas Wittmann
# 
Dear R users,

i try to integrate lgamma from 0 to Inf. But here i get the message "roundoff error is detected in the extrapolation table", if i use 1.0e120 instead of Inf the computation works, but this is against the suggestion of integrates help information to use Inf explicitly. Using stirlings approximation doesnt bring the solution too.

## Stirlings approximation
lgammaApprox <- function(x)
{
  0.5*log(2*pi)+(x-(1/2))*log(x)-x
}

integrate(lgamma, lower = 0, upper = 1.0e120)
integrate(lgammaApprox, lower = 0, upper = 1.0e120)
1.374051e+242 with absolute error < 3.2e+235
1.374051e+242 with absolute error < 3.2e+235

integrate(lgamma, lower = 0, upper = Inf)
integrate(lgammaApprox, lower = 0, upper = Inf)
Fehler in integrate(lgamma, lower = 0, upper = Inf) : 
  roundoff error is detected in the extrapolation table
Fehler in integrate(lgammaApprox, lower = 0, upper = Inf) : 
  roundoff error is detected in the extrapolation table


Many thanks if you have any advice for me!

best regards

Andreas
--
5 days later
Stavros Macrakis
# 
On Wed, Apr 22, 2009 at 3:28 AM, Andreas  Wittmann
<andreas_wittmann at gmx.de> wrote:
Both gamma and log are positive and monotonically increasing for large
arguments.

What can you conclude about the integrability of log(gamma(x))?

          -s