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# Tag Info

### Series vs Asymptotic in 12.1

Extended comment, I won't accept this as an answer. Here are some cases I've found where Series might be a better choice than ...
Accepted

### How could this asymptotic expansion be obtained?

Exact expression for $\sigma_n$: b[n_] = BesselJ[1, BesselJZero[0, n]]*BesselJZero[0, n]*StruveH[0, BesselJZero[0, n]]; σ[n_] = π/2*(-1)^n*(b[n + 1] - b[n]); ...
Accepted

...
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### Asymptotic expansion around infinity for inverse cdf of normal distribution

Using assumptions and an immediate assignment: ...
Accepted

### AsymptoticSum does not give any output

How about analytically evaluating the product Product[1 + (3/(4 n)), {n, 2, j}] \frac{\Gamma \left(j+\frac{7}{4}\right)}{\Gamma \left(\frac{11}{4}\right) \Gamma (...

### Asymptotic inverse function?

@Roman's answer is exactly what you asked for, but as a check, here is a second answer using Bessel's series expansion for the solution of the Kepler equation: ...
Accepted

### Not getting the correct asymptotic behaviour when sending a small parameter to zero

You could try using AsymptoticSolve instead: ...
Accepted

Try this: ...

Execute ...
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### Determinant of matrix with asymptotic expansion

The O representation of an expansion point of Infinity is obtained with: O[x, Infinity] (...
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### Asymptotic[] Doesn't Actually Compute

tao2 = (2*(-(1/4)/E^(2*t^2) + Pi/8 - ((1/4)*Sqrt[Pi]*t)/E^t^2 + (1/4)*Pi*Erf[t] - ((1/4)*Sqrt[Pi]*t*Erf[t])/E^t^2 + (1/8)*Pi*Erf[t]^2))/Pi; ...
Accepted

### AsymptoticDSolveValue returing input

The ode ode = eps y''[x] + (x + x^3)*y'[x] - 2*y[x] == 0 ode /. y->(y[-#]&) (* -2 y[-x] - (x + x^3) Derivative[y][-x] +eps (y^\[Prime]\[Prime])[-x] == 0*) ...
Accepted

### Asymptotics and limits of second order ODE which depend on (two) parameters

You could find the solution $h(x)$ and then use Asymptotic on its derivative? ...

### AsymptoticIntegrate of a difficult integral

Edit: there's a factor of 2 missing from the RHS of the $\sin(\sin x)$ relation, which follows from a mistake/typo in the Maths.S.E answer for which I provided a ...
Accepted

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

Here's a symbolic solution, whose asymptotic expansion may be obtained: ...

### When to use Series vs Asymptotic?

The definition of Asymptotic can be accessed by GeneralUtilities`PrintDefinitionsLocal, and it seems that part of its code ...

### Is there a way to check whether $f(x)=o(g(x))$ for given $f$ and $g$?

Another pre V11.3 method is to use the limit definition: littleO[f_, g_, x_, x0_:Infinity] := PossibleZeroQ[Limit[f/g, x -> x0]] littleO[x, x^2, x] ...

### How to study asymptotic behavior, built-in functions

Another possibility is to use new in M12 function AsymptoticSolve: sol = AsymptoticSolve[y==f[r],y,{r,Infinity,4}] ...

### Finding Asymptotics for a Series

As @DanielLichtblau says, Mathematica can do the symbolic sum in terms of LerchPhi: sum = Sum[2^i/i, {i, n}] -I ([Pi] - I 2^...

### AsymptoticDSolveValue multiple solutions

DSolve does not find $y(x)=x$ either, and I think this is why AsymptoticDSolveValue does not. I am sure they share some core ...
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### Asymptotic inversion of ExpIntegralEi function

You got correct hints on Math.SE. Define: E1[z_] := EulerGamma - ExpIntegralEi[-z]; E2[z_] := -ExpIntegralEi[-z] Exp[z]; They can be inverted like this ...
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### Selecting the negative expression

Select negative solutions. Select[sols, Resolve[Exists[ϵ, ϵ > 0, ForAll[s, Pi - ϵ < s < Pi, (t /. # /. Theta -> s) < 0]]] &] <...

### AsymptoticDSolveValue returing input

Mathematica can not do it. May be because it is boundary value problem. Compare ...
Accepted

### Asymptotic Output Tracking: Code Issues

Updated answer Use the chain rule and express $f'[t]$ in terms of $x'[t]$. Then the two equations can be solved for $x'[t]$ and $H'[t]$. AffineStateSpaceModel (...