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Results tagged with asymptotics
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user 8060
6
votes
4
answers
426
views
Is it possible to have the asymptotics of this function?
Is there any hope to obtain the asymptotics ?
Thanks in advance. …
- 1,021
3
votes
3
answers
176
views
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
$$x \log (x)-(x+n) \log (x-n)=0$$
$$x_n^{(0)}=n+\sqrt n+\frac 14 \log(n)+\frac 12 \tag 1$$ …
- 1,021
5
votes
2
answers
138
views
Looking for the asymptotics of an asymptotics
The problem is to find the asymptotics of $t$, solution of the implicit equation
$$\color{blue}{\left(1-2 x^2\right) \text{erfc}\left(\left(\frac{1}{2}+t\right)
x\right)+\text{erfc}\left(\left(\frac … It seems that I would need to use very large $p$ to obtain a good asymptotics of the asymptotics if I stay with this procedure. …
- 1,021
2
votes
Looking for the asymptotics of an asymptotics
After @MariuszIwaniuk's comment and answer
$$e^{-2 x^2 t}=\frac 1{1-2x^2}\,\,\frac{2t+1}{2t-1}\sim \frac {1+4t}{2x^2-1}\quad \implies \quad t=-\frac 14+\frac 1{2x^2}W\left(\frac{1}{2} e^{\frac{x^2}{2 …
- 1,021
11
votes
1
answer
376
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} \ …
- 1,021