Does converge for all ? If it does, it's not too hard to show that it equals when is odd and when is even. Is always eventually going to grow much faster than no matter how large is ?
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Originally Posted by Random Variable Does converge for all ? If it does, it's not too hard to show that it equals when is odd and when is even. Is always eventually going to grow much faster than no matter how large is ? As , increases more slowly than any positive power of x. Thus and therefore which is enough to ensure convergence of your integral at ∞. There is also a singularity at 0. But near 0 the integral looks like , and that also converges.
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