Questions tagged [asymptotics]
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106 questions
4
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Numerical Integration of Highly Oscillatory Functions with Bessel Kernels
I have met a integral in my research with Bessel Kernels and Hypergeometric functions.
The codes are
...
- 2,420
4
votes
2
answers
274
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Help with asymptotics on an interesting sum
I recently learned an interesting limit and was trying to understand the asymptotics. Unfortunately I'm getting nowhere.
Take ...
- 43
1
vote
1
answer
155
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How do we find an asymptotic approximation of the function $\mathbf{P}(r)=\left(t_1+\prod\limits_{k=1}^{r}(t_2+k^{s})\right)^n$?
Suppose we have the following function, where $s\in\mathbb{R}$ and $t_1,t_2,n\in\mathbb{N}\cup\{0\}$ are constants:
$$\mathbf{P}(r)=\left(t_1+\prod_{k=1}^{r}(t_2+k^{s})\right)^n$$
Question: What is ...
- 51
1
vote
2
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180
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Finding leading order behaviour of an integral
There is an integral whose leading order behaviour in terms of $p$ is what I want.
$$I(p) = \int_0^{D(p-1)} \log(1-Q^2e^{-x}) \, \mathrm dx,$$
where $D$ is really large and $p$ tends to 1.
For the ...
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5
votes
2
answers
445
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Find asymptotic values of ODE solution
I study the various curves obtained with Frenet-Serret equations,
using this code:
...
- 2,710
0
votes
0
answers
106
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AsymptoticSolve returns the input
I have the following input
Assuming[\[Epsilon] != 0,
AsymptoticSolve[q^3 (q - 2) - (h - (1/\[Epsilon])^2) == 0,
q, {h, 0, 2}]]
which returns
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- 231
3
votes
2
answers
179
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Expanding the HypergeometricPFQ function gives complex values
I have a function
HypergeometricPFQ[{}, {2, 2}, -Log[n]]
which for real n > 0 gives a real values, as can be seen on the ...
- 3,553
1
vote
0
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82
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How to use Mathematica to calculate the asymptotic variance of the sample interquartile range?
How to use Mathematica to calculate the asymptotic variance of the sample interquartile range?
Is the below code correct?
...
- 1
3
votes
1
answer
303
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Is there a way to automate the generation of these polynomials?
The motivation of this question is pure curiosity.
Working on this problem, I tried to find the zero of function
$$f(x)=m\,(m-1)^{\frac{1}{m}-1}\, x^{1-\frac{1}{m}}+x-1 \quad \quad \text{where} \...
- 1,105
0
votes
0
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Finite Element Method Limiting boundary condition
I am trying to solve this PDE using FEM
[![PDE][1]][1]
[![Solution][2]][2]
with this bc:
$$
\lim_{y\to\infty}\big\{ \psi(x, y) - v(y)\big\} =\psi^0(x),\lim_{x\to\pm\infty}\big\{ \psi(x, y) - \psi^0(x)\...
- 21
2
votes
1
answer
157
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Approximate solution to second order homogeneous differential equation with variable coefficients
I hope to obtain an approximate solution to the following second-order homogeneous differential equation with variable coefficients, where $\frac{1}{2}\leq H\leq 1$ and $t\geq0$, $i$ is imaginary unit:...
- 303
0
votes
0
answers
135
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Why doesn't AsymptoticDSolveValue return a result for my system of equations?
I’m new to asymptotic analysis, and I’m trying to solve a system of differential equations outlined in this book (pp.269-271). However, when I attempt to solve it, Mathematica doesn’t return a result. ...
- 416
3
votes
1
answer
241
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Looking for *probably* strange asymptotics
Trying to answer this question in Mathematics Stack Exchange, I made the conjecture that for any $a>1$
$$\underset{n\to \infty }{\text{limit}}\Bigg(A_n(a)=\frac{\sum _{k=1}^{n } \left(a^k \tan^{-1}(...
- 1,105
0
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0
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152
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How to Collect terms with some unknown forms?
I'm working on an instability problem. The minimum of my code is
...
- 35
0
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2
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212
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Asymptotic: Issue with constant term of Asympotic of rational function
Here is a simple function to show the issue:
f[x_] := 3 x + 2 + 2/(x + 1)
It is very clear from this expression that the asymptote for ...
- 2,740