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Results tagged with sequences-and-series
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user 120939
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
6
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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
1
vote
0
answers
47
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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 $ …
1
vote
1
answer
88
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A scaled random walk on the number line
An agent $A$ is performing a random walk on the number line. Let $X_t$ be his position at time $t$. $X_{t+1}$ is calculated according to the following rules:-
$ X_{t+1} =$
\begin{cases}
…
0
votes
1
answer
132
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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
votes
1
answer
154
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Is this recurrent sequence 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 $ …