# Tag Info

Accepted

### Calculating relative error of Ramanujan formula for ellipse perimeter

We have to express a parameter $h=(a-b)^2/(a+b)^2$ in terms of the eccentricity of the ellipse $e = \sqrt{1-b^2/a^2}$. Similarly we need comparing the second Ramanujan approximation for the ...
• 57.5k
Accepted

### Series expansion not working with $\sqrt{1-x^d}$

Perhaps this?: Asymptotic[Sqrt[(1 - u)], {u, 0, 2}] /. u -> x^d (* 1 - x^d/2 - x^(2 d)/8 *) If we examine the output of ...
• 237k
Accepted

### Why does Mathematica get the infinite sum of this representation of the taylor series of $\cos^2(x)$ wrong?

Expanding on the comment by @Goofy and after reading the docs we see that: "ParallelFirstToSucceed" try each method in parallel until one succeeds ...
• 16.1k

### Discrepancy with Hurwitz Zeta function

HurwitzZeta When calculating a sum one can choose an option GenerateConditions -> True to get appropriate conditions on parameters for convergence of a series <...
• 57.5k

### Evaluating series expansion is very slow

One can try breaking the expression into pieces: ...

### Evaluating series expansion is very slow

For alternative algorithm and for speed up you can may use: NSeries: ...
• 14.2k
Accepted

### First argument -h is not a valid variable

h is a local to Series, you cannot use it as a functionargument. Try ...
• 54.5k

### Find Generalized Series with Symbolic Variable

With SeriesCoefficient, the order and expansion point can be symbolic. ...
• 160k

### Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

Yes, Mathematica is able to do that. ...
• 54.5k

### Asymptotic integral expansion at infinity

Solving this problem analytically is difficult. However, it is possible to get exact values of the integral In in symbolic form for each ...
• 3,094

### Find Generalized Series with Symbolic Variable

If I understand correctly what you want the following is your friend ...
• 16.1k
Accepted

...
• 160k

### Series expansion of a given function

I am not sure why this is happening, but here's a quick fix. Do a replacement $\xi_3 \rightarrow \tfrac{1}{x_3}$ and then expand around $\infty$. ...
• 16.1k
Accepted

### Getting coefficients list of a series expansion at a point different from 0

One way is to do the following: expand to whatever order you want, and subsequently substitute $x-1$ by $y$. Do CoefficientList in the ...
• 16.1k
Accepted

...
• 160k

### Set the value of a parameter in a Series expression

For others struggling I figured it out. Just use Normal@Series when doing the expansion. Then you can use $/.e\rightarrow 1$ without issue.
Accepted

### How to find the asymptotic envelope of a function?

The Series command of 14.0 on Windows 10 produces the required answer for BesselJ[n,x] ...
• 27k
Accepted

### How to invert a series with two variables, where the series is expanded in the other variable?

You can use AsymptoticSolve for this purpose: ...
• 131k

### Series expansion of a given function

Use Assuming. ...
• 1,471
Accepted

### How to obtain a list of pairs of exponents in a double series expansion?

Using CoefficientRules, Normal and SortBy: ...
• 25.7k
Accepted

### Comparing two power series and extracting their coefficients

In sum2, the powers of x and y are less than or equal to 6, whereas in ...
• 23.9k

• 3,887
Accepted

### Asymptotic solution of a system of ODEs

A simple approach is to introduce the ansatz $$f(u)=\sum_{k\ge0}\frac{f_k}{u^k},\qquad a(u)=\sum_{k\ge0}\frac{a_k}{u^k}$$ which you plug into the ODE and solve for the coefficients. I find \begin{...

...
• 160k
Accepted

### Expanding polynomials using valuation

Maybe: Min[CoefficientRules[#[[2]], x][[All, 1, 1]]] + #[[1, 1]] \[Lambda]0 & /@ CoefficientRules[poly, \[Lambda]] (* {2 \[Lambda]0, 1} *) Or: ...
• 3,277
Accepted

...

### Series expansion not working with $\sqrt{1-x^d}$

Since the expansion is at an analytic point of the function, the power series is a Taylor expansion: $$S(x)=\sum_{n=0}^{\infty} \frac{\frac{d^n}{dx}(1-x^d)^{1/2}}{n!}x^n$$ However when $d$ is ...
• 2,432
1 vote
Accepted

### Finding constant term in product expression

You may use "Expand" to get the expanded form of your polynomial. And then "Cases" can pick the constant terms. here is an example. First we create some large polynomial: ...
• 53k

Only top scored, non community-wiki answers of a minimum length are eligible