**Infinite series**Hi:
We have the following identity:
\sum_{m=1}^{infinity} (-1)^m/((2m-3)^2*(2m-1)*(2m+1)^2)=-Pi/32.
When we type the command,
In[1]:=Sum[(-1)^m/((2*m-3)^2*(2*m-1)*(2*m+1)^2),{m,Infinity}]
we get
2 1 1
-16 Pi + 2 Pi - HurwitzZeta[2, -(-)] - Zeta[2, -]
4 4
Out[1]= --------------------------------------------------
512
The command Simplify[%] does not simplify it further.
I am sure the above expression must be equal to -Pi/32, ...

**Infinite series**Is anyone out there familiar with using MATLAB to manipulate infinite series
calculations and where do I go to find?...cmw.
...

**Re: Infinite series**On 12/15/09 at 7:27 AM, jogc@mecheng.iisc.ernet.in (Dr. C. S. Jog)
wrote:
>We have the following identity:
>\sum_{m=1}^{infinity} (-1)^m/((2m-3)^2*(2m-1)*(2m+1)^2)=-Pi/32.
>When we type the command,
>In[1]:=Sum[(-1)^m/((2*m-3)^2*(2*m-1)*(2*m+1)^2),{m,Infinity}]
>The command Simplify[%] does not simplify it further.
>I am sure the above expression must be equal to -Pi/32, but a user
>would prefer this answer than the above one.
There are a variety of reasons Simplify often does not achieve
what you are looking for. But the obvious thing to try when...

**Mathematica and infinite series**Hi,
I am about to embark on a project that operates heavily in infinite
series, so I started figuring out Mathematica's basis capabilities. I
found them very impressive, but I came across this:
f[x_] := Sum[Log[n]/(n^2 Factorial[n]) x^n, {n, 1, Infinity}]
Assuming[n > 0, SeriesCoefficient[f[x], {x, 0, 4}]]
Answer:
SeriesCoefficient[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(
\*SuperscriptBox[\(x\), \(n\)]\ Log[n]\), \(
\*SuperscriptBox[\(n\), \(2\)]\ \(n!\)\)]\), {x, 0, 4}]
Why doesn't Mathematica produce Log[n]/(n...

**How to solve this infinite series...**The cosine function can be evaluated by the following
infinite series:
cos x = 1 – [x^2 / 21] + [x^4 / 41] – [x^6 / 61] ……
Write a Matlab function to implement this formula so that it
computes and prints out the values of cos(x) as each term in
the series is added. In other words, compute and print in
sequence the values for:
cos x = 1
cos x = 1 - [x^2 / 21]
cos x = 1 - [x^2 / 21] + [x^4 / 41]
In article <fnlmg7$9g7$1@fred.mathworks.com>,
Melvin <melvin1974@mathwoks.com> ...

**infinite series #2**New to MATLAB. Trying to write code to determine the covergence value
of an infinite series. I also need to display to 5 sig. fig. Any help
would be appreciated.
Thanks, Danny
Danny Little wrote:
>
>
> New to MATLAB. Trying to write code to determine the covergence
> value
> of an infinite series. I also need to display to 5 sig. fig. Any
> help
> would be appreciated.
>
> Thanks, Danny
Take a look at the function symsum, from the Symbolic Math toolbox.
Nilton Quoirin wrote:
>
>
> Danny Little wrote:
>>
>>
>> New to MATLAB. Trying to w...

**How to solve this infinite series... #2**The cosine function can be evaluated by thefollowing
infinite series:
cos x = 1 – [x^2 / 21] + [x^4 / 41] – [x^6 / 61] ……
Write a Matlab function to implement this formula so that it
computes and prints out the values of cos(x) as each term in
the series is added. In other words, compute and print in
sequence the values for:
cos x = 1
cos x = 1 - [x^2 / 21]
cos x = 1 - [x^2 / 21] + [x^4 / 41]
In article <fnqlf2$lmp$1@fred.mathworks.com>,
Melvin <melvin1974@mathwoks.com> w...

**A model problem for infinite series**Hi,
As a follow up to my previous post and to give a little bit more
information, I would like to briefly describe a mathematically
nonsensical problem which has some of the elements that I need.
To solve Laplace's equation for u(r, alpha) on the unit circle subject
to Dirichlet boundary conditions U(alpha), one needs to decompose U as a
Fourier series, multiply each term by r^|n| and add them back up.
The model problem is this. Starting with a boundary condition U0, solve
for u and let U1(alpha) = du/dr(evaluated at r=1)*f[alpha], where
f[alpha] is relatively simple a...

**Can Mathematica do this (infinite series)?**Hi,
I'm working on a project involving infinite series and I don't know how
to do it or even ask a sensible question about it. So I cooked up a
question the answer to which might give me ideas.
f[x_]:=Sum[c[n]x^n, {n, 1, Infinity}]
What's the infinite series for
f[x]^2 + Sin[x]f[x]
in terms of c[n]?
What's the simplest way that Mathematica can answer this question for
general c[n]?
The pipe dream is this:
f[c_][x_] := Sum[c[n] x^n, {n, 1, Infinity}]
g[c_][x_] := f[c][x]^2 + Sin[x] f[c][x]
d[c_][n_] := SeriesCoefficient[g[c][x], {x, 0, n}]
...