# Questions tagged [asymptotics]

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### MMA does not provide the correct asymptote for an integral function

Given is the function $$f(x)=\int_0^\infty \mathbb{exp}\left(-\frac{x^2}{2t^2}-t\right)\mathbb{d}t$$ Mathematica returns for the asymptotic behavior $x\to\infty$ using ...
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### Mathematica can't simplify asymptotic expressions containing constant symbols

I want to calculate simple asymptotic expressions involving positive constant symbols ($a > 0$), such as $$\lim_{x\to\infty} \operatorname{sech}(a x) \sim 2 e^{-a x}$$ Surprisingly, the ...
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### Asymptotic Relation as Boundary Condition

I want to solve a system of non-linear second order differential equations. For some of the unknown functions there are boundary conditions that i know how to write them in Mathematica. One of the ...
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### AsymptoticSolve for the Inverse

How can I find an asymptotic expansion for the inverse of the function $f[x]=x(1+x^{1/4})$ near $0$? I tried substituting $z=x^{1/4}$ and using AsymptoticSolve to ...
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### AsymptoticDSolveValue multiple solutions

I'm trying to solve the following ODE asymptotically. $$y(x)^2 y'(x)^2-\left(\sqrt{2} x\right)^2 y'(x)^2+y(x)^2=0$$ From ...
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### Does AsymptoticSum work with Arithmetical Number Theoretic Functions?

The recent function AsymptoticSum works as follows: AsymptoticSum[1/k, {k, 1, n}, n -> \[Infinity]] with expected result: ...
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### Series vs Asymptotic in 12.1

The functionality of Series and Asymptotic (new in V12.1) is very similar. In fact, they are both listed in the Asymptotics ...
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### Why can we only find the asymptotic expression of the solution of the first implicit function?

Here are three implicit function equations ...
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### Determinant of matrix with asymptotic expansion

i have determinant which each element have asymptotic expansion. $\begin{bmatrix}1+5/s+6/s^3+O[1/s^4] & 1+8/s+4/s^2+O[1/s^4]\\1+2/s+2/s^3+O[1/s^4] & 1-1/s+8/s^3+O[1/s^4]\end{bmatrix}$ ...
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### 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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### AsymptoticLess function confusion

I have an algorithm which complexity is: ...
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 $$\sigma_n=(1)^n\frac{\pi}{2} \big( j_{0,n+1} \,... 1answer 216 views ### Solving for the recursion relation for the expansion coefficients of the asymptotic expansion of an ODE I want to solve for the asymptotic solution of the following differential equation$$ \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$$as y\... 0answers 171 views ### Asymptotes of parabolic cylinder differential equations with boundaries at infinity For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which ... 1answer 98 views ### Functional operations with data [closed] I have the following data (a shorter sample of the whole data) : ... 0answers 71 views ### Discordance between the results of AsymptoticIntegrate and calculations Mathematica 11.3 finds r = Integrate[Cos[k*(x^4 - x)], {x, -Infinity, Infinity}, Assumptions -> k > 0] ... 2answers 168 views ### Finding series expansion of solution of algebraic equation I have the following algebraic equation: ... 2answers 68 views ### Is there a way to check whether f(x)=o(g(x)) for given f and g? I would like a way to check, for two arbitrary but specified real analytic functions f(x) and g(x), whether f(x)=o(g(x)). I am using "little-o notation," where f(x)=o(g(x)) is true if and ... 1answer 129 views ### AsymptoticIntegrate with multiple integration variables? I wanted to find the asymptotic form of$$\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 ...
How can I find a simple expression that's asymptotic to $\sum_{i=1}^{n-1}2^i/i$? That is, Sum[2^i/i,{i,1,n-1}]. According to https://reference.wolfram.com/...