I was wondering how the remainder of the stirling formular behaves for $ n \rightarrow \infty $, while $n$ is the index of the bernoulli polynomial.
I got a problem either way: if it diverges then how can wolfram alpha print something like:
http://mathworld.wolfram.com/StirlingsSeries.html at (7)
it seems as they wrote for $ n \rightarrow \infty $ but then where is the remainder term? if it doesnt diverge the sterling series in (7) would have to be convergent which isnt true. i was wondering in general how one gets from the euler mclaurin formula to the stirling formula as in (7) the only way i see is when the remainder becomes zero for $ n \rightarrow \infty $.
can you tell me how the remainder term actually behaves for $ n \rightarrow \infty $?