Questions tagged [convergence]
The convergence tag has no usage guidance.
21
questions
2
votes
0answers
46 views
Total convergence of a function series [migrated]
Let us consider the following function series:
$$ \sum_{n=1}^{\infty} \frac{1}{n^x + n^{-x}}.$$
It seems that there is total convergence in $(- \infty, -1-\delta] \cup [1+ \delta, + \infty)$ for $\...
3
votes
2answers
84 views
Does this sum converge, and why?
Mathematica says the following sum
Sum[(mm Gamma[mm])/
Gamma[-(1/2) + mm] - (mm^(3/2) - (3 Sqrt[mm])/8 - (7 Sqrt[1/mm])/
128), {mm, 1, \[Infinity]}]
...
0
votes
1answer
60 views
Laplace Transform - Differentiation in Time property demonstration
I have a signal
x[t_]=t/3 Exp[-3t] UnitStep[t]
and the laplace transform as
...
0
votes
1answer
89 views
$\sum_{n=1}^{+\infty}\frac{\cos(\frac{n\pi}{2})}{n}$ gives wrong answer in Mathematica? [closed]
I wanted to compute $\sum_{n=1}^{+\infty}\frac{\cos(\frac{n\pi}{2})}{n}$ on Mathematica and it says the sum does not converge, even though it does by Dirichlet's test. When I plugged the same sum in ...
0
votes
2answers
33 views
How to eliminate error: Numerical integration converging too slowly
While doing numerical integration, I am getting a result with the following error messages:
...
6
votes
2answers
109 views
Convergence Rate of NDSolve by Increasing the Spatial Grids
I have a very simple PDE equation, with an analytical solution (exact solution). And I want to play with NDSolve and increasing the number of Spatial Grids.
Here is the exact solution:(Analytical ...
1
vote
1answer
83 views
How can I determine the convergence rate of recurrence methods?
I want to solve the equation $x^{3}-x-1=0$ by iterating recurrence equations.
I have two different recurrence relations for solving this equation:
$x_{k+1}=\sqrt[3]{x_{k}+1} \quad(k=0,1, \cdots)$
$...
asked Oct 1 '20 at 2:20
A little mouse on the pampas
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2
votes
2answers
166 views
How to judge whether the series is absolutely convergent?
I need to judge whether the series $\sum_{n=1}^{\infty}(-1)^{n}\left(1-\cos \frac{\alpha}{n}\right)$ (Ī±>0) is absolutely convergent.
...
asked Sep 1 '20 at 3:15
A little mouse on the pampas
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0
votes
1answer
65 views
Why is the function `SumConvergence` not valid for simple power series
I want to find the convergence interval of function $\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{x^{n}}{n}$.
...
asked Aug 22 '20 at 1:43
A little mouse on the pampas
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0
votes
1answer
143 views
How to get the convergence radius of the result of Series? [duplicate]
The Taylor expansion of function is very useful, but the convergence radius of power series results after Taylor expansion is also important. But the result of ...
asked Aug 12 '20 at 4:04
A little mouse on the pampas
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0
votes
1answer
76 views
How to verify whether the abnormal integral is convergent or divergent?
How to verify the convergence and divergence of the abnormal integrals $\int_{0}^{1} \frac{\sqrt[m]{\ln ^{2}(1-x)}}{\sqrt[n]{x}} d x$:
...
asked Aug 12 '20 at 1:29
A little mouse on the pampas
5,0422 gold badges9 silver badges27 bronze badges
6
votes
1answer
200 views
Improving mesh and NDSolve solution convergence
I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
1
vote
1answer
55 views
Speeding up simultaneous numerical integration where some integrals vanish
I would like to carry out a number of numerical integrals in the form of a table:
...
0
votes
0answers
89 views
Plotting a complex integral function [duplicate]
Can anybody help me to plot the T1 and T2, please?
The problem is that the integral part becomes so huge or indeterminate at ...
3
votes
2answers
279 views
Code that produces plot in V5 doesn't work in later versions
I have problem in plotting Integral function.
I can compute/plot the graph of this integration below in Mathematica 5.0, but it is not possible to plot it in higher Mathematica versions.
My code is:
<...
1
vote
0answers
60 views
Why doesn't Mathematica provide an answer while Wolfram|Alpha does, concerning a series convergence?
Among other series I've been working on, I was asked to find whether
$$\sum_n 1-\cos(\frac{\pi}{n})$$
converged, and Mathematica's output to ...
0
votes
0answers
37 views
Nintegrate providing results much smaller than what is expected
This is the first time I am posting something here. So, apologies if I make any mistake. I am dealing with a numerical integration in Mathematica-11.0 that has a Bessel function in it. In order to ...
5
votes
2answers
755 views
Bug in Integrate?
In v. 11.1.0.0 Mathematica for Linux
Integrate[Sin[Cosh[t]], {t, 0, Infinity}]
returns
Integrate::idiv: Integral of Sin[Cosh[t]] does not converge on {0,[...
5
votes
1answer
197 views
Wolfram Language 12 says this absolutely convergent series does not converge. Is there any similar example?
I am reading "Lectures on complex function theory" by Takaaki Nomura.
In this book, there is the following example:
$\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converges absolutely.
But ...
6
votes
1answer
324 views
Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$
In this sum over $k$
Sum[Sin[k (k - 1)]/k, {k, 1, ā}]
the result still containes the summation index $k$.
...
1
vote
1answer
289 views
Repeated convergence test failure and why?
i have assigned all the values and the ODE assigned is as this
...
