# Questions tagged [asymptotics]

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### Looking for the asymptotic solution of $x \log (x)-(x+n) \log (x-n)=0$

Working this problem on Mathematics Stack Exchange, I very quickly obtained as an estimate of $x$ solution of $$x \log (x)-(x+n) \log (x-n)=0$$ $$x_n^{(0)}=n+\sqrt n+\frac 14 \log(n)+\frac 12 \tag 1$$ ...
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### AsymptoticSum does not give any output

I am trying to get leading terms in terms of $p$ of the following expression $\sum_{j = p+2}^{\infty} \frac{\sqrt{\Pi_{n=2}^{j} (1+(0.75/n)) }}{\sqrt{j}(1+j)}$. I know that this sum converges and is ...
• 185
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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 ...
261 views

### 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 ...
454 views

### Asymptotic inversion of ExpIntegralEi function

I'm looking at the small-x and large-x asymptotic expansions of the inverse of exponential integral $E_1$ (https://dlmf.nist.gov/6.2#E1) \begin{array}{lll} E_1 & = & \int_z^\infty \frac{e^{-...
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223 views

### Solution of a nonlinear equation depending on the parameter

I need to solve an equation Solve[m + x*(-1 + 2*x - Log[2*Pi]) + (-1 + 2*m - 4*x)*x*Log[x] == 0, x] It is not possible on a symbolic level. It would be ideal to ...
• 3,094
1 vote
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### Asymptotic Output Tracking: Compensator properties

Asymptotic Output Tracking: Code Issues The question is, rather, of a theoretical nature (practical applications can be viewed in the topic at the link). Asymptotic Output Tracking is said to be based ...
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### Question on AsymptoticDSolveValue

I would like to use AsymptoticDSolveValue to solve following type of equations at infinity y''[x] + (1 - 1/x^s) y[x] == 0 where ...
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I am trying to solve an ODE which looks like this: $t^2*f'(t)+K.f(t)+t*G.f(t)=0$ for $K$ and $G$ some matrices 2*2 and $f$ is a vector of functions in variable $t$. ...