Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [asymptotic]

The tag has no usage guidance.

6
votes
1answer
227 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
89 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
70 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
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
votes
1answer
92 views

Functional operations with data [closed]

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

Finding series expansion of solution of algebraic equation

I have the following algebraic equation: ...
3
votes
2answers
62 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
58 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 ...