Quick Limit

1. Sep 14, 2006

bomba923

For what values of k would
$$\mathop {\lim }\limits_{x \to \infty } \frac{{\Gamma \left( {kx + 1} \right)}} {{x^{kx} }}$$
converge?

Last edited: Sep 14, 2006
2. Sep 14, 2006

CRGreathouse

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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