I have the series
$\sum_{n=0}^{\infty}(-1)^{n}a_{n}(\nu)\frac{\sin[\nu\,(m-n)]}{\nu\,(m^2-n^2)}=\frac{1}{m}$,
where $m$ is an integer. Is it possible to compute the coefficients $a_{n}(\nu)$? An exact solution is found for $\nu=\pi$:
$a_0=1, a_{n}=2\times(-1)^n$.
It is related to a w...
It is well-known that one can evaluate the sum
$$\sum_{k =1}^{N-1} \csc^2\left(\pi \frac{k}{N} \right)=\frac{N^2-1}{3}.$$
The answer to this problem can be found here
click here.
I am now interested in the more difficult problem of evaluating for some $j \in \{1,...,N-1\}$ the sum (we do no...
How can I determine all integer points of the following equation
$$y^2=x^3+10546$$
I tried Magma with
IntegralPoints(EllipticCurve([0,10546]));
but got the answer that it "could not determine the Mordell-Weil group." What are my options here?
0
An element $a$ of a Lie algebra $L$ is called a Fredholm element if the adjoint operator $ad_a:L \to L$ is a Fredholm linear map.That is: its kernel is a finite dimensional space and its range $ad_a(L)$ is a finite codimensional space.
Is there an infinit dimensional Lie algebra with at least on...
In mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations. It is named in honour of Erik Ivar Fredholm.
A Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional kernel
ker
T
{\displaystyle \ker T}
and (algebraic) cokernel
c
o
k
e
r
T
=
Y
/
r
a
n...
