Das hat Konsequenzen, z.B. den bei der Herleitung der Gaußverteilung verbundenen Übergang von absolutenWahrscheinlichkeiten zu Wahrscheinlichkeitsdichten.
Eine noch genauere Näherung, die aber nicht mehr leicht herleitbar ist und schon für x £ 10 ganz gut ist, gibt die folgende Version der Stirlingschen Formel
www.tf.uni-kiel.deUsing the Strirling formula you may, e.g., move from absolute probabilities ( always a number between 0 and 1 ) to probability densities ( any positive number ) without being aware of it.
Finally, an even better approximation exists (the prove of which would take some 20 pages) and which is already rather good for small values of x, say x > 10:
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