infinite sum: $sum_{m=1}^{infty}frac{sin^2(frac{mpi}{gamma_n})}{(m^2-n^2gamma_n^2)^2}$
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I've been told to repost this.
The problem I'm working on is finding the following infinite sum:
$$sum_{m=1}^{infty}frac{sin^2(frac{mpi}{gamma_n})}{(m^2-n^2gamma_n^2)^2}$$
where $ninmathbb{N}^+$ (i.e. a positive natural number) and $gamma_n=1+frac{1}{4}cos(n)$
sequences-and-series
asked Nov 20 at 22:19
Michael Cloud
816
add a comment |
up vote
0
down vote
favorite
I've been told to repost this.
The problem I'm working on is finding the following infinite sum:
$$sum_{m=1}^{infty}frac{sin^2(frac{mpi}{gamma_n})}{(m^2-n^2gamma_n^2)^2}$$
where $ninmathbb{N}^+$ (i.e. a positive natural number) and $gamma_n=1+frac{1}{4}cos(n)$
sequences-and-series
asked Nov 20 at 22:19
Michael Cloud
816
$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I've been told to repost this.
The problem I'm working on is finding the following infinite sum:
$$sum_{m=1}^{infty}frac{sin^2(frac{mpi}{gamma_n})}{(m^2-n^2gamma_n^2)^2}$$
where $ninmathbb{N}^+$ (i.e. a positive natural number) and $gamma_n=1+frac{1}{4}cos(n)$
sequences-and-series
asked Nov 20 at 22:19
Michael Cloud
816
I've been told to repost this.
The problem I'm working on is finding the following infinite sum:
$$sum_{m=1}^{infty}frac{sin^2(frac{mpi}{gamma_n})}{(m^2-n^2gamma_n^2)^2}$$
where $ninmathbb{N}^+$ (i.e. a positive natural number) and $gamma_n=1+frac{1}{4}cos(n)$
sequences-and-series
sequences-and-series
asked Nov 20 at 22:19
Michael Cloud
816
asked Nov 20 at 22:19
Michael Cloud
816
edited Nov 20 at 23:01
asked Nov 20 at 22:19
Michael Cloud
816
asked Nov 20 at 22:19
Michael Cloud
816
asked Nov 20 at 22:19
Michael Cloud
816
816
$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09
add a comment |
$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09
$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09
add a comment |
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$n$ is fixed? ${}$
– Clayton
Nov 20 at 22:34
n can be any positive natural number, but yes, as far as the sum over m is concerned, its some fixed number
– Michael Cloud
Nov 20 at 23:00
@Michael Cloud Do you accept solution what consists of Lerch-transcendents?
– JV.Stalker
Nov 21 at 18:09