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9 votes
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 ...
Michael E2's user avatar
  • 237k
4 votes

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 $\infty$. ...
bmf's user avatar
  • 16.1k
4 votes
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 ...
bmf's user avatar
  • 16.1k
3 votes

Series expansion of a given function

Use Assuming. ...
Jie Zhu's user avatar
  • 1,471
2 votes

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 ...
josh's user avatar
  • 2,432
1 vote
Accepted

Find radius of convergence for two series product

For any complex analytic function the radius of convergency of its series expansion around a point $z_0$ is the distance to the nearest singularity. So by complex analytical combinations of two or ...
Roland F's user avatar
  • 3,887

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