# Questions tagged [asymptotics]

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### For function f(x) = c / (3x+1) , what value of c is the 2nd function also asymptotic to (1/x) as x → ∞

for what value of c is the 2nd function also asymptotic to x1 as x → ∞ in the picture attached
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### Computing Asymptotics of a Fresnel Integral At Infinity

I am very new to Mathematica, and am trying to write code that will give me the series asymptotics for the function $$F(y) = \int_0^y f(y)\;dy,$$ where $f(y) = y^2 \cos(y^2) C( (2/\pi)^{1/2} y)^2$, ...
125 views

### When to use Series vs Asymptotic?

I'm confused about the difference between Series and Asymptotic. Is there a good rule of thumb of when to use which? ...
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### AsymptoticDSolveValue

this is the first time ever i am posting a problem on ANY forum as i am desperate to find asymptotic approximation to this problem with any boundary or initial condition please see if you can help ...
1 vote
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### Asymptotic Solver for Nonlinear Singular Perturbations

I would like to ask if there are any built-in functions / packages that allow one to obtain asymptotic expansions for nonlinear singular perturbations. More specifically, I am dealing with ...
117 views

### Can Mathematica estimate this complex function?

Mathematica has given me a function in $x,r$ given by ...
1 vote
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### How to preserve the order of expressions in the asymptotic expansion?

I have a complicated expression involving logarithms. ...
262 views

### Is there any possibility of obtaining an asymptotic approximation (instead of numerical solutions) of such a 2nd-order homogeneous ODE in Mathematica?

Here is a typical linear ordinary differential equation with variable coefficients: $$\ddot{x\hspace{0pt}}(t)+\left(\frac{\ln t}t\right)^{\!2}x(t)=0\text.$$ Now I intend to investigate the (leading) ...
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### Asymptotics and limits of second order ODE which depend on (two) parameters

Dear Mathematica community, for this second order ODE: h''[x] Sinh[2 x] + h'[x] 2 Cosh[2 x] - 2 h[x] Tanh[x] == 0, which is basically the harmonic equation for ...
38 views

### AsymptoticSolve for Taylor Expansion of Implicit Function

I have an implicit function ...
118 views

### Is there something faster than AsymptoticDSolveValue for getting the terms in a power series solution?

Here's an example of a differential equation which Mathematica 13.1 just returns without solving ...
1 vote
196 views

### AsymptoticDSolveValue returing input

I would like to find a uniform approximation of the solution to the boundary layer problem $$\epsilon y'' + (x+x^3)y'-2y=0, \hspace{20mm}y(1)=y(-1)=1$$ When using AsymptoticDSolveValue, I inputted the ...
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### Prevent the use of a specific function in an output

I am trying to asymptotically integrate a function with the code AsymptoticIntegrate[Exp[I k x + I/5 k^5], {k, 0, Infinity}, x -> Infinity] and the output is ...
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### Selecting the negative expression

Let Theta,t be real variables and Phi an expression of ...
64 views

### Asymptotic expansion for a function containing irrational exponents

I'm trying to find an asymptotic expansion of a function containing irrational exponents in the form of a power series (which also might contain irrational exponents). It works correctly if I request ...
379 views

### Asymptotic inverse function?

A paper I am reading defines a variable $\theta$ in terms of another variable $\phi$ as an expansion in $u$, where $u$ is understood to be small: $$\theta=\phi-u^2\sin\phi+\mathcal{O}(u^4).$$ They ...
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### Asymptotic does not give asymptotic?

Expression Asymptotic[Exp[(1 + E^x)/(1 + x)], x -> Infinity] gives Exp[(1 + E^x)/x] as the answer but these functions are ...
178 views

### 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 ...
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### Asymptotic solve question

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

### Successive solutions using previously found [closed]

is there a way to use previous calculated values of solve? solving equations based on asymptotic expansion $x^2+x-\varepsilon=0$ $x=x_0+\varepsilon x_1 + \varepsilon^2 x_2 + \varepsilon^3 x_3$ ...
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### 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 $r\longrightarrow \infty$...
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### 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: ...
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### 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 : $$g(t)= c\int_{0}^{1-t} t^{m-1}\left[(u+t)^{m}-u^{m}\right]^{n-2}(u+t)^{m-1} d u$$ ...
313 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
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### “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 ...
194 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
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### 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 ...