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Results tagged with exponential-sums
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user 120939
The method of exponential sums is one of a few general methods enabling us to solve a wide range of miscellaneous problems from the theory of numbers and its applications. The strongest results have been obtained with the aid of this method. Therefore knowledge of the fundamentals of theory of exponential sums is necessary for studying modern number theory.
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Summing the infinite series $\sum_{k=0}^{\infty} \frac{x^k}{(k!)^2}$ [closed]
Is there a closed form sum of
$\sum_{k=0}^{\infty} \frac{x^k}{(k!)^2}$
It is trivial to show that it is less than $e^x$ but is there a tighter bound?
Thanks
0
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1
answer
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Prove that the following running average is monotonically decreasing
Let $S_n$ be defined as $\frac{1}{n}\sum_{t=1}^{t=n} [x^2+(p-q)x]$ where $x = 1-(1-p-q)^t$. We want to find the conditions on $p$ and $q$ such that $S_n$ is monotonically decreasing for all $n$. $0 < …
1
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0
answers
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Find conditions for the following running average to be monotonically decreasing
Let $S_n$ be defined as $\frac{1}{n}\sum_{t=1}^{t=n} [px_t^2 - (p+q)x_t]$ where $x_t = 1-(1-p-q)^t$. We want to find the conditions on $p$ and $q$ such that $S_n$ is monotonically decreasing for all $ …