All Questions
Tagged with recursion series-expansion
12
questions
3
votes
2
answers
222
views
Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?
I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
- 63
0
votes
0
answers
82
views
How to do this recursion relation in Mathematica effectively?
I have a function $h_{\Delta,l}(r,\eta)$ satisfying
\begin{equation}
h_{\Delta,l}(r,\eta)=\tilde{h}_{l}(r,\eta)+\sum_{k}\frac{c(k)}{\Delta-(1-l-k)}r^{k}h_{1-l+k,l+k}(r,\eta)
\end{equation}
where $k$ ...
- 101
0
votes
1
answer
79
views
Trouble while trying to re-run open source code
I am a physics student and this is my first time working with Mathematica. I am trying to run the notebook mentioned here, titled "Amplification factors of the superradiant scattering of a ...
- 83
1
vote
2
answers
156
views
Recursive sequence with RecurenceTable
I want to compute elements of a recursive sequence and use them as coefficients of a power series. However, the (i+1)-th element depends on all previous elements. Writing this as a sum in ...
- 123
0
votes
0
answers
63
views
Recurrence relation of coeeficients of power series solution to DE
Say I have a DE
$$
-\phi \left(\phi \left(\left(6975 \phi ^2-3704 \phi +160\right) \omega '(\phi )+\phi
\left(\left(6975 \phi ^2-4688 \phi +266\right) \omega ''(\phi )+\phi \left(2
\left(...
- 203
0
votes
2
answers
404
views
Getting the coefficients of a series that solves a differential equations
I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation
...
- 3
1
vote
3
answers
165
views
Why doesn't Mathematica evaluate the series with recursion relationship as expected?
I define a series $dg(i)$ as the $i$th derivative of a function $g[t]$ for $i>0$ and known the first term $dg(1)=(t-x)g(t)$. In mathematica, the code is:
...
- 195
2
votes
1
answer
356
views
Solving for the recursion relation for the expansion coefficients of the asymptotic expansion of an ODE
I want to solve for the asymptotic solution of the following differential equation
$$ \left(y^2+1\right) R''(y)+y\left(2-p \left(b_{0} \sqrt{y^2+1}\right)^{-p}\right) R'(y)-l (l+1) R(y)=0$$
as $y\...
- 181
4
votes
2
answers
228
views
Problems with ContinuedFractionK
I am interested in calculating the following series
$$
\sum_{k=0}^{+\infty}{ \frac{ x^k }{\, a (a+1) \cdots (a+k) \,} }
$$
using this continued fraction (I expect) equivalent form:
$$
\cfrac{1}{a + ...
- 1,101
6
votes
3
answers
1k
views
How can I make Mathematica return a series expansion in the form $\sum_{j=0}^\infty \dots$ instead of $a_0 + a_1x^1 + \dots + a_{n-1}x^{n-1}+ O(x^n)$
I have a function
$$\phi(x) = \sqrt{(x-t)^2 + c^2},$$
and I want an asymptotic expression for it as $x \to \infty$.
Using the following code I can calculated such an expression:
...
- 339
3
votes
2
answers
708
views
How to simplify output of Series?
The command
Series[Sum[Sum[1/(a*b), {b, a, 3 a}], {a, 1, N/Sqrt[3]}, Assumptions -> N > 0], {N, Infinity, 1}]
produces a somewhat complicated answer
<...
- 27.3k
4
votes
1
answer
424
views
Computing a series in terms of exponential function
Is there any way to compute the following series in terms of exponential function ?
$$\sum_{k=0}^\infty Y_1(k)\;x^k$$ where
$$Y_1(k) = \frac{(k - 1)!}{k!}Y_3(k - 1)$$
$$Y_2(k) = \frac{(k - 1)!}{k!}...
- 155