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Quick Limit

  1. Sep 14, 2006 #1
    For what values of k would
    [tex]\mathop {\lim }\limits_{x \to \infty } \frac{{\Gamma \left( {kx + 1} \right)}}
    {{x^{kx} }} [/tex]
    Last edited: Sep 14, 2006
  2. jcsd
  3. Sep 14, 2006 #2


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    Certainly for k < 0 it diverges, since gamma is ill-behaved there. For k > e it also diverges by Stirling's approximation. There's the easy part! I'll have to think about the remaining (0, e]. (It obviously converges for k = 0.)
    Last edited: Sep 14, 2006
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