# Questions tagged [asymptotics]

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### Can Mathematica solve an ode asymptotically as x goes to infinity?

Given the following ode for $x\rightarrow\infty$: $$\left(x f(x)^3 \left(\frac{(x f^\prime)^\prime}{x}\right)^\prime\right)^\prime=0,$$ in the sense of "asymptotics", the equal sign is ...
61 views

### Asymptotic solve question

I am trying to find the asymptotic solution of the following differential equation- ...
113 views

### How can I calculate the asymptotic value of this function correctly?

I'm trying to reproduce the results of a paper which in one part of it, I have to calculate the asymptotic value of a function but I can't reproduce that result exactly. I will be so grateful if ...
62 views

### Successive solutions using previously found [closed]

is there a way to use previous calculated values of solve? solving equations based on asymptotic expansion $x^2+x-\varepsilon=0$ $x=x_0+\varepsilon x_1 + \varepsilon^2 x_2 + \varepsilon^3 x_3$ ...
78 views

### Non Linear Differential Equation Asymptotics

I wish to study the asymptotic behaviour of the following equation: $\frac{d^2 a}{dr^2} = 2 a(r) \phi(r)^2 + B_1 a(r) (1-\phi^2(r) + B_2 a(r)^2)$ $\phi(r)\longrightarrow 1$ as $r\longrightarrow \infty$...
84 views

### How to reproduce Asymptotic Bounds of Recurrences in Wolframalpha

In Wolframalpha's Examples for Recurrences, there are bunch of Asymptotic Bounds of Recurrences examples, like this It can get perfect result: ...
31 views

### The average of a random varible with pdf in the form of a parametric integral

The pdf of a random variable $T$ in the interval $(0,1)$ in a certain problem I am trying to solve is given by : $$g(t)= c\int_{0}^{1-t} t^{m-1}\left[(u+t)^{m}-u^{m}\right]^{n-2}(u+t)^{m-1} d u$$ ...
167 views

### Asymptotic Solve

I am trying to solve a set of equations in Mathematica. My input is Solve[y*x - 1/x - 1/x^2 == 1 && z*x - 1/x^2 + 1/x == 2, {y, z}] and output is ...
1 vote
64 views

### “Largest” symbolic common factor of an integer sequence (not simply GCD)

Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
153 views

### How is this asymptotic expansion of an integral calculated?

I am strongly impressed by this example from New in 13 as = AsymptoticIntegrate[ (t^10 + 3) Exp[I λ (t^5 + t + 1)], {t, -2, 2}, {λ, Infinity, 2} ] <...
1 vote
52 views

### Are these solutions correct using AsymptoticDSolveValue? Less::nord: Invalid comparison with I attempted

Should one worry about correctness of these solutions due to the messages they generate? Or can one safely ignore these messages? Example 1 ...