I would like to find the number of all points with integer coordinates ($(x,y,z): x,y$ and $z$ integer) in an ellipsioid
$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2} < P $
Is it possible to find an equation for the number of them, and how?
I encountered this problem while solving a physics...
The unknown functions $f_1(t)$ and $f_2(t)$ are the solutions of the following system of dual integral equations
\begin{align}
\int_0^\infty \mathrm{d}\lambda \, \lambda^{-\frac{1}{2}} J_{1}(\lambda r)
\int_0^1 \mathrm{d}t \Big( \left( 1 + e^{-\lambda}(\lambda-1) \right) J_{\frac{3}{2}} (\lambda...
[integer-relation] only has two uses, and neither usage seems to use the tag properly. I suggest we remove this tag (I don't know the protocol for this, please let me know if this is not how one should do this).
Likewise, [invariant-measure] has one use, and that too is a PSQ.
Could anyone tell me what does it mean by discrete, Lebesgue singular and absolutely continuous parts of an invariant measure?
Also, by example, could anyone help me to understand, how a measure can be uniquely decomposed into two-measure?
Thanks for helping!
Could anyone tell me how to show the (a) following line integral is of independent of the path?
$$I= \int_C[(3y^2+\pi^3\cos x)i+(6xy-3\pi^3\sin y)j]\cdot dr$$, where $C$ is a curve connecting the point $P(-\frac{\pi}{2}, \pi)$ to $Q(\pi,\pi)$
(b) How to find a potential function and use that to...
