I would like to approximate $ \ln(\sum_{k=0}^n(n-2k)^p) $ Here $p\geq 2$
Approximating the logarithm of sum
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sequences-and-series
approximation
1 Answers
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Presumably the upper limit should be $n/2$ to avoid powers of negative numbers (particularly problematic if $p$ isn't an odd integer). I would convert to an integral: $\sum_{k=0}^n(n-2k)^p \approx \int_{k=0}^{n/2}(n-2k)^p\;dk$ which yields to the substitution $u=n-2k$.
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0@SauravTomar: Once the integral is evaluated, one can take the log. – 2012-04-29