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What can be said about the sum $f(x) = \sum_{m=1}^{\infty} e^{-x\sqrt{m}}\cos(x\sqrt{m})$ for $x>0$?

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#summation #exponential-sum
474
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Big Oh Bound on Double Exponential Summation

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#summation #asymptotics #exponential-sum
334
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Prove the following series $\sum\limits_{s=0}^\infty \frac{1}{(sn)!}$

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#sequences-and-series #trigonometry #exponential-sum
44
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For what x does $P_c(x) = \sum^\infty_{n=0} (-1)^{n+1}\cdot n\cdot x^n$ converge?

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#real-analysis #sequences-and-series #exponential-sum
73
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Calculate growth constant given start, end and number of periods

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#calculus #exponential-sum
67
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How to prove that $f(x)$ is equal to $ \frac{1}{2}(\exp(x) -\exp(-x)) $?

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#functions #exponential-sum
164
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Finding the maximum of an exponential sum

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#derivatives #optimization #exponential-function #approximation #exponential-sum
1.4k
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Solving limits with ln without L’Hôpital’s rule

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#limits #logarithms #limits-without-lhopital #exponential-sum
275
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Changing the order of summation and integration

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#integration #summation #permutations #combinations #exponential-sum
203
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Gauss Sum calculation

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#characters #exponential-sum #gauss-sums
298
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Solving an inequality with a variable in the exponent and that same variable multiplied by the base of the exponent?

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#sequences-and-series #inequality #exponentiation #problem-solving #exponential-sum
36
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Inequality regarding summation and exponentation

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#linear-algebra #inequality #summation #exponential-sum
328
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Amount of real numbers, in a given sequence, whose fractional part lies in a given closed interval

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#analysis #analytic-number-theory #exponential-sum #additive-combinatorics
55
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subgroups of $\mathbb{Z}_N^k$

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#group-theory #finite-groups #cyclic-groups #exponential-sum
100
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q-exponentials, Convolution and Multiplication

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#probability-theory #probability-distributions #convolution #exponential-sum #q-analogs

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