Questions tagged [asymptotic]

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17 views

AsymptoticLess function confusion

I have an algorithm which complexity is: ...
7
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1answer
230 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
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1answer
93 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
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0answers
81 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 ...
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0answers
24 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
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1answer
92 views

Functional operations with data [closed]

I have the following data (a shorter sample of the whole data) : ...
0
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2answers
74 views

Finding series expansion of solution of algebraic equation

I have the following algebraic equation: ...
3
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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
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1answer
59 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 ...