Questions tagged [asymptotics]
The asymptotics tag has no usage guidance.
11
questions
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0answers
41 views
Asymptotic bound of $\sum_{i=0}^{\log(n)} 2^{i} \sum_{k=0}^{\frac{n}{2^{i}}} (k+2)^{2} + \theta(n)$ [migrated]
What is the asymptotic bound for $\sum_{i=0}^{\log(n)} 2^{i} \sum_{k=0}^{\frac{n}{2^{i}}} (k+2)^{2} + \theta(n)$?
0
votes
1answer
69 views
Asymptotic solution of a second-order ODE containing InverseFunction
Essentially, I have a second-order differential equation given by ode below. In order to solve it, I need to obtain an asymptotic solution where $g(x)$ must vanish at infinity which will be used after ...
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0answers
18 views
8
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1answer
234 views
How could this asymptotic expansion be obtained?
I must precise that I am a very limited user of Mathematica (I can only run it from time when going at university).
Working this problem, I found that
$$\sigma_n=(1)^n\frac{\pi}{2} \big( j_{0,n+1} \,...
2
votes
1answer
106 views
Solving for the recursion relation for the expansion coefficients of the asymptotic expansion of an ODE
I want to solve for the asymptotic solution of the following differential equation
$$ \left(y^2+1\right) R''(y)+y\left(2-p \left(b_{0} \sqrt{y^2+1}\right)^{-p}\right) R'(y)-l (l+1) R(y)=0$$
as $y\...
2
votes
0answers
87 views
Asymptotes of parabolic cylinder differential equations with boundaries at infinity
For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which ...
0
votes
0answers
26 views
Inverting the asymptotic expansion of Gauss Hypergeometric Function
I am interested in obtaining the asymptotic expansion of $r(\rho)$ (which is the inverse of the object rho[r_,b_,q_] below). Basically I want to series expand rho[r_,b_,q_] for large $r$ (i.e. as $r\...
-1
votes
1answer
92 views
Functional operations with data [closed]
I have the following data (a shorter sample of the whole data) :
...
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2answers
81 views
Finding series expansion of solution of algebraic equation
I have the following algebraic equation:
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3
votes
2answers
64 views
Is there a way to check whether $f(x)=o(g(x))$ for given $f$ and $g$?
I would like a way to check, for two arbitrary but specified real analytic functions $f(x)$ and $g(x)$, whether $f(x)=o(g(x))$.
I am using "little-o notation," where $f(x)=o(g(x))$ is true if and ...
3
votes
1answer
65 views
AsymptoticIntegrate with multiple integration variables?
I wanted to find the asymptotic form of
$$\int_0^1\mathrm{d}x\int_0^1\mathrm{d}y\,\mathrm{e}^{M(x-1/2)^2+M(y-1/2)^2}$$
for $M\rightarrow\infty$. I tried
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